1- 23- 4If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A =01 -4and b =- 135 - 1115- 3Find a single vector x whose image under Tis b.Is the vector x found in the previous step unique?O A. Yes, because there is a free variable in the system of equations.B. No. because there are no free variables in the system of equations.OC. No. because there is a free variable in the system of equations.O D. Yes, because there are no free variables in the system of equations. Determine which matrices are in reduced echelon form and which others are only in echelon form.1 400 00 0110 1110 100 40 4 4b. 0 1 1 0c.0 0 0 220 0 0 0 30 0 100 0 0 10 0 0 1Is matrix a in reduced echelon form, echelon form only, or neither?reduced echelon formechelon form onlyneitherIs matrix b in reduced echelon form, echelon form only, or neither?reduced echelon formechelon form onlyneitherIs matrix c in reduced echelon form, echelon form only, or neither?echelon form onlyreduced echelon formneither

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1 - 2 3 - 4 If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A = 1 -4 and b = - 13 5 - 11 15 - 3 Find a single vector x whose image under T is b. Is the vector x found in the previous step unique? A. Yes, because there is a free variable in the system of equations. B. No, because there are no free variables in the system of equations. O C. No, because there is a free variable in the system of equations. D. Yes, because there are no free variables in the system of equations.

1 - 2 3 - 4 If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A = 1 -4 and b = - 13 5 - 11 15 - 3 Find a single vector x whose image under T is b. Is the vector x found in the previous step unique? A. Yes, because there is a free variable in the system of equations. B. No, because there are no free variables in the system of equations. O C. No, because there is a free variable in the system of equations. D. Yes, because there are no free variables in the system of equations.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

1
- 2
3
- 4
If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A =0
1 -4
and b =
- 13
5 - 11
15
- 3
Find a single vector x whose image under Tis b.
Is the vector x found in the previous step unique?
O A. Yes, because there is a free variable in the system of equations.
B. No. because there are no free variables in the system of equations.
OC. No. because there is a free variable in the system of equations.
O D. Yes, because there are no free variables in the system of equations.

Determine which matrices are in reduced echelon form and which others are only in echelon form.
1 40
0 00 0
110 11
10 10
0 40 4 4
b. 0 1 1 0
c.
0 0 0 22
0 0 0 0 3
0 0 10
0 0 0 1
0 0 0 1
Is matrix a in reduced echelon form, echelon form only, or neither?
reduced echelon form
echelon form only
neither
Is matrix b in reduced echelon form, echelon form only, or neither?
reduced echelon form
echelon form only
neither
Is matrix c in reduced echelon form, echelon form only, or neither?
echelon form only
reduced echelon form
neither

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-4 4. -6 If T is defined by T(x)= Ax, find a vector x whose image under Tis b, and determine whether x is unique. Let A= 0 1-3 and b= - 18 4 -17 16 -3 Find a single vector x whose image under T is b.
What are the values of h for which the vectors are linearly dependent? HEH O a. The vectors are linearly dependent if and only if h = -1 O b. There are no values of h for which the vectors are linearly dependent, as the vectors are linearly independent Oc The vectors are linearly dependent if and only if h = 2 O d. The vectors are linearly dependent if and only if h = -16 O e The vectors are linearly dependent for all values of h. Of. The vectors are linearly dependent if and only if h = -10 O g. None of the answers is correct O h. The vectors are linearly dependent if and only if h = -3
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