Answers
Answer:
[tex]\left[\begin{array}{cccc}-1\\1\\1\\0\end{array}\right][/tex], [tex]\left[\begin{array}{cccc}0\\2\\0\\1\end{array}\right][/tex] Are two vectors which are basis of null space of A
Step-by-step explanation:
Basis of a null space is a vector matrix which when multiplied by the reduced echelon form of the matrix gives null matrix or 0 matrix
So, to find the reduced echelon form we apply the row operations :
R₁ = R₁/2
[tex]\left[\begin{array}{cccc}1&-2&3&4\\2&-1&3&2\\4&-5&9&10\\0&-1&1&2\end{array}\right][/tex]
R₂ = R₂ - 2R₁
[tex]\left[\begin{array}{cccc}1&-2&3&4\\0&3&-3&-6\\4&-5&9&10\\0&-1&1&2\end{array}\right][/tex]
R₃ = R₃ - 4R₁
[tex]\left[\begin{array}{cccc}1&-2&3&4\\0&3&-3&-6\\0&3&-3&-6\\0&-1&1&2\end{array}\right][/tex]
R₂ = R₂/3
[tex]\left[\begin{array}{cccc}1&-2&3&4\\0&1&-1&-2\\0&3&-3&-6\\0&-1&1&2\end{array}\right][/tex]
R₁ = R₁ + 2R₂
[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&3&-3&-6\\0&-1&1&2\end{array}\right][/tex]
R₃ = R₃ - 3R₂
[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&0&0&0\\0&-1&1&2\end{array}\right][/tex]
R₄ = R₄ + R₂
[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&0&0&0\\0&0&0&0\end{array}\right][/tex]
which is a reduced echelon form of the matrix A
now ,
[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&0&0&0\\0&0&0&0\end{array}\right][/tex] [tex]\left[\begin{array}{cccc}x1\\x2\\x3\\x4\end{array}\right][/tex] [tex]=\left[\begin{array}{cccc}0\\0\\0\\0\end{array}\right][/tex]
therefore,
x₁ + x₃ = 0
x₁ = -x₃
x₂ - x₃ - 2x₄ = 0
x₂ = x₃ + 2x₄
so now replacing values of x₁ , x₂ in the vector matrix
[tex]\left[\begin{array}{cccc}-x3\\x3 + 2x4\\x3\\x4\end{array}\right][/tex]
we can write the above matrix as,
[tex]x3\left[\begin{array}{cccc}-1\\1\\1\\0\end{array}\right][/tex] [tex]+ x4\left[\begin{array}{cccc}0\\2\\0\\1\end{array}\right][/tex]
therefore we can say that above mentioned vector matrices are the basis of the null space of matrix A
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Related Questions
A line passes through the point (5,-11) and has slope of -2.
Find an equation of this line.
y = -2x – 1
y = 5x – 11
y = 5x – 2
y = -2x – 11
Answers
Answer:
y=-2x -1
Step-by-step explanation:
(y-y1) = m(x-x1)
y-(-11) = -2(x-5)
y+11 = -2x + 10
subtract 11 on both sides thus
y = -2x -1
Six angles of a heptagon have measures of 80°, 90°, 100°, 145°, 165° and 170°. The smallest of all the exterior angles measures ____.
80°
150°
190°
10°
Answers
Answer: 10°
Step-by-step explanation:
Since an exterior angle and its corresponding interior angle are supplementary, meaning they have a fixed sum, to minimize the exterior angle, we need to maximize the interior angle.
This means we need to consider the 170° interior angle, so the corresponding exterior angle is 10°.
What single transformation was applied to triangle A to get triangle B?
Choose 1 answer:
Translation
Rotation
Reflection
Dilation
Answers
Triangle LMN is congruent to triangle FGH, as shown.
Go
65
Mark this and return
5-
4
3
321
2-
-6-5-4-3-2-14 2 3 4 5 6
یہ ب
-2
-3
FL
4
5
6
H
X
What is the length of side LM?
units
Next
Submit
Answers
Answer: 5
Step-by-step explanation:
If [tex]\triangle LMN \cong \triangle FGH[/tex], this means that [tex]\overline{LM} \cong \overline{FG}[/tex] by CPCTC.
Using the distance formula,
[tex]FG=\sqrt{(-3-0)^{2}+(-4-0)^{2}}=5\\\\\therefore LM=\boxed{5}[/tex]
A
Find the value of x.
Round to the nearest tenth.
19°
B
142°
X
x = [?]
Law of Sines: sin A
42
sin B
b
sin C
C
Answers
The value of x will be equal to x = 79.
What is the triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
For an isosceles triangle, the value of two opposite angles is equal and the opposite sides are also equal.
The Sum of the three angles is equal to 180 degrees so the third angle will be calculated as:-
Angle = 180 - 142 - 19 = 19
Now applying Lami's theorem in the triangle we will get the third side.
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
[tex]\dfrac{Sin 19}{42}= \dfrac{Sin142}{x}[/tex]
[tex]x = \dfrac{42\times Sin 142}{Sin19}[/tex]
x = 79
Therefore the value of x will be equal to x = 79.
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Answer:
Step-by-step explanation:
Give the “best” big-oh notation to describe the complexity of the algorithm that prints all bit strings of length n.
Answers
It is correct to state that a bit can be in one of 2 states, either 1 or 0.
What is a bit?A bit is is a single binary digit. A bit can either be "1" or "0".
What is the explanation to the above answer?We stated that It is correct to indicate that a bit can be in one of 2 states, either 1 or 0. This indicates that 2ⁿ strings must be created in total. The string must then be processed twice.
The first time, for generation andThe second for reading.Hence, Our time is now O(2ⁿ⁺¹) = O(2ⁿ)
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1. Which graph describes the relation {(1, 2), (1, -2), (−1, 2), (-2, 0)}?
Answers
Answer:
The first graph
Step-by-step explanation:
The second graph does not have a point at (1, -2).
Find the average rate of change of the function f(x) - 2x² + 6x + 6, from x=-3 to x=-1. Note, the directions are equivalent to "Find the average rate of change over the interval [-3,-1]".
Answers
Answer: -2
Step-by-step explanation:
I will assume you meant [tex]f(x)=2x^{2}+6x+6[/tex].
[tex]f(-3)=2(-3)^2 + 6(-3)+6=6\\\\f(-1)=2(-1)^2 + 6(-1)+6=2\\\\\therefore \frac{f(-3)-f(-1)}{-3-(-1)}=\frac{6-2}{-2}=\boxed{-2}[/tex]
Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A.3
B.5
C.7
D.9
E.4
Answers
a rhombus has perimeter 120 M and one of its diagonal is 50 M find the area of the Rhombus
Answers
The area of the rhombus is 829.1562m².
What is the area of the rhombus?A rhombus is a four sides quadrilateral with the four sides equal in length
The area of a rhombus = [tex]\frac{1}{4}d[/tex] ×√(p² - 4d²)
where p is the perimeter and d is the diagonal
1/4(50) x √(120² - 4 x 50²) =829.1562m²
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Please help whilst I try to solve this as well.
Answers
Answer:
420
Step-by-step explanation:
Answer:
V = 340 cm3
Step-by-step explanation:
Calculate the volume of the prism without the gap, then subtract the volume of the gap.
[tex]V=(5)(10)(8)-(3)(2)(10)=400-60=340cm^{3}[/tex]
Hope this helps
The number of measles cases has increased by 5.3% since 2000.
Express your answer rounded correctly to the nearest hundredth.
Stated another way, the number of measles cases is
times what it was in 2000.
Express your answer rounded correctly to the nearest tenth of a percent.
Stated another way, the number of measles cases was
% of what it is now.
Answers
The expressions for the number of measles are y = a(1.05)^x and y = a(1.1)^x
How to express the number of measles?Let the initial number of measles in 2000 be represented as:
Initial = a
The rate of increase is given as:
Rate, r = 5.3%
The number of measles in x years after 2000 is represented as:
y = a * (1 +r)^x
Substitute r = 5.3%
y = a * (1 + 5.3%)^x
So, we have:
y = a * (1 + 0.053)^x
Evaluate the sum
y = a * (1.053)^x
To express to the nearest hundredth, we approximate to 2 decimal places
y = a(1.05)^x
To express to the nearest tenth, we approximate to 1 decimal place
y = a(1.1)^x
Hence, the expressions for the number of measles are y = a * (1.05)^x and y = a * (1.1)^x
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PLEASE HELPP!!!!!
Question 9 of 13
Which of the following scatterplots represents the data shown below?
(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47),
(9,34), (10,3), (11, 33), (12, 35)
Answers
The attached graph below can represent the scatter plot of the points. the correct option is B.
How to find the function which was used to make graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
Given:
(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47), (9,34), (10,3), (11, 33), (12, 35)
The above points would be plotted using the following scale such as:
x: axis -> 1 interval = 10 units
y: axis -> 1 interval = 10 units
The attached graph below can represent the scatter plot of the points. the correct option is B.
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find the y-component of this vector
leave an explanation for brainlest
Answers
The y- component of the vector is 18.31728 m
What is Vector?A quantity that has both magnitude and direction but not position.
The y- component is
Dy = 18.6* sin80
Dy = 18.6* 0.9848
Dy= 18.31728 m
Hence, the y- component of the vector is 18.31728 m.
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Mary Lou received $5,000 from her grandparents for her college education 8 years prior to her enrolling in college. Mary Lou invested the money at 5.5% compounded semiannually. How much money would she have in her savings account when she is ready to enroll in college? A: The balance in her account would be $__________ when she is ready to enroll in college. (Round your answer to the nearest cent.)
Answers
Answer:
The total amount , principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 5.5% per year compounded 2 times per year over 8 years is $7,717.55.
Step-by-step explanation:
Compound interest is based on the principal amount and the interest that accumulates on it in every period.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
First, convert R as a percent to r as a decimal
r = R/100
r = 5.5/100
r = 0.055 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 5,000.00(1 + 0.055/2)^(2)(8)
A = 5,000.00(1 + 0.0275)^(16)
A = $7,717.55
The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 5.5% per year compounded 2 times per year over 8 years is $7,717.55.
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The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. suppose intensity is 8000 units at a distance of 2 miles. what will the intensity be at a distance of 11 miles? round your answer to the nearest unit.
The answer is B. 222 Units
Answers
Graph the line passing through (6, 1) whose slope is m = 3.
Answers
Answer: [tex]y=3x-17[/tex]
Step-by-step explanation:
use point-slope form:
[tex]y_{1} -y=m(x_{1} -x)[/tex]
[tex]y-1=3(x-6)[/tex]
[tex]y-1=3x-18[/tex]
[tex]y=3x-17[/tex]
Answer:
equation: y = 3x - 17
[image attached]
Step-by-step explanation:
we know that the equation for a line is y = mx + b
we are given a point, (6, 1)
remember that a point is (x, y)
we can plug these sample x and y values into our equation, replacing x and y
y = mx + b
1 = m6 + b
we know that m = 3 [this was a given], so we can plug this into our equation
1 = (3)(6) + b
1 = (18) + b
1 = 18 + b [we can now solve for "b"]
1 = 18 + b
-18 - 18
-17 = b
so, we can re-write our equation so that we can graph it:
y = 3x - 17
we can now plug in x-values to graph this:
(you'll see these written in the table on the graph)
y = 3(0) - 17
y = -17
y= 3(1) - 17
y = 3 - 17
y = -14
y = 3(2) - 17
y = 6 - 17
y = -11
y = 3(3) - 17
y = 9 - 17
y = -8
y = 3(4) - 17
y = 12 - 17
y = -5
y = 3(-1) - 17
y = -3 - 17
y = -20
y = 3(-2) - 17
y = -6 - 17
y = -23
y = 3(-3) - 17
y = -9 - 17
y = -26
[there is an image attached of my graph]
hope this helps!! :)
A geometric seqerence 1.5, -3, 6, -12 .... How many regative terms in the sequencs greater than
- 6000 ?
Answers
The total negative terms are 4 which are greater than -6000 if the geometric sequence 1.5, -3, 6, -12 ... with a common ratio -3.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
A geometric sequence 1.5, -3, 6, -12 ....
The common ratio r = -3/1.5 = -2
1.5, -3.6, 6, -12, 36, -108, 324, -972, 2916, -8748
The total negative terms = 4
Thus, the total negative terms are 4 which are greater than -6000 if the geometric sequence 1.5, -3, 6, -12 ... with a common ratio -3.
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Select the graph that represents two quantities in a proportional relationship
Answers
The correct answer is option D.It is the graph that represents two quantities in a proportional relationship.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
As we can see graph D is showing the correct proportionality. We can also create an equation of proportionality as:-
Y = 2x
Put y = 0.5
0.5 = 2 x 0.5 = 1
As we put y=0.5 we get the value of x = 1 as shown in the graph.
Therefore the correct answer is option D.It is the graph that represents two quantities in a proportional relationship.
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PLEASE ANSWER THIS AS FAST AS POSSIBLE!
The steps a student took to solve an equation are shown below.
3/4 (-8x+20)= -8(-x-3)
STEP 1: -6x+15=8x+24
STEP 2: 15=2x+24
STEP 3: -9=2x
STEP 4: x= -9/2
What error did the student make? PLEASE EXPLAIN THE ANSWER
What is the correct value of x?
PLEASE SHOW WORK!
Answers
Between Steps 1 and 2, the student added 6x to the left hand side, but subtracted 6x from the right hand side.
Given the graph, find the initial value of the domain [ ___, 2].
Answers
Answer:
Looks to me like it should be -2
HELPPPPPPPPPPPP plssss -. A bag of cookies cost the cookie company $.50 to make, but the local grocery store sells the same bag of cookies for $4.50. How much does the local grocery store mark up the price of the bag of cookies?
Answers
Answer:
$4
Step-by-step explanation:
Company $0.50
Store. $ 4.50
Price up $ X
4.50
- 0.50
------------
4.00
X= $4.00
Enlarge the shape on scale factor 0
Answers
Answer:
Multiply with 2 to the original sides
What is the value of
(X+Y) (X-Y) when x=3.5,y=-8.7
Answers
Answer:
[tex](x + y)(x - y)[/tex]
[tex](3.5 - 8.7)(3.5 + 8.7)[/tex]
[tex](-5.2)( 12.2)[/tex]
[tex]-63.44 [/tex]
Given f(x)=2x^2-1 and g(x) =3x-5 what is f-g
Answers
[tex]f(x)-g(x)=(2x^{2}-1)-(3x-5)=2x^{2}-1-3x+5=\boxed{2x^{2}-3x+4}[/tex]
Which of the numbers below are whole numbers? Check all that apply.
A. 734.895
B. 0.7538
C. 7
D. 5429.97
E. 616
F. 401119.8
Answers
Answer:
7, 616 because there is no floating point
An administrator is asked to file papers in a box which has the following dimensions height 15cm width 30cm and depth 20cm. Calculate the volume of the box.
Answers
The volume of the box is 9000 square cm if the box has the following dimensions height of 15cm width 30cm and depth of 20cm
What is a cuboid?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
We have:
An administrator is asked to file papers in a box that has the following dimensions height of 15 cm width of 30 cm and depth of 20 cm.
Let L be the length
W be the width
H be the height of the box:
Given:
L = 20 cm
W = 30 cm
H = 15 cm
The volume of the box
= 15×30×20
9000 square cm
Thus, the volume of the box is 9000 square cm if the box has the following dimensions height of 15cm width of 30cm, and depth of 20cm
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What is the product?
2 3
5 9 -1 -7
11 5 -3
10 15 20
45 -5 -35
55
10
4 2
55
7
14
25 -15
45 -1 -7
315
+7 9
CO
8
9
4 1-2
Answers
Answer:
A.
Step-by-step explanation:
Hello, this is what we call matrix. multiplication matrix to be precised.
so it is;
5×2=10
5×3=15
5×4=20
5×9=45
5×-1= -5.
5×-7= -35
5×11=55
5×5=25
5×-3= -15.
i hope you understand. That is matrix for you but it has different categories
Simplify (27-17)^2-80
Answers
Answer:
-60
Step-by-step explanation:
Solve the equation for x.
2(x + 4) = 2
5
x = [?]
Answers
Answer:
x=1
Step-by-step explanation:
(2(x+4))/5=2
Multiply both sides by 5
2(x+4)=10
Divide both sides by 2
x+4=5
subtract 4 from both sides
x=1
