suppose tha 3 -3 2 [:] 4 -2 A = and B 5 1 3 -1 3 2 -2 -1 Given the following descriptions, determine the following elementary matrices and their inverses a. The elementary matrix E¡ multiplies the first row of A by 1/4. E ,E, ' %3D b. The elementary matrix E, multiplies the second row of A by -4. E2 ,E,' c. The elementary matrix Eg switches the first and second rows of A. Eg ,E,' d The elementary matrix E. adds 3 times the first row of A to the second row of A

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.4: Determinants
Problem 53PS
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Question
Suppose that:
3 -3 2
4
-2
A =
and B =
5 1
3
-1 3
2 -2 -1
Given the following descriptions, determine the following elementary matrices and their inverses.
a. The elementary matrix E, multiplies the first row of A by 1/4.
E
1
b. The elementary matrix E, multiplies the second row of A by -4.
E2
‚E,
c. The elementary matrix Ez switches the first and second rows of A
E3
E
d. The elementary matrix E, adds 3 times the first row of A to the second row of A.
1
E4
Transcribed Image Text:Suppose that: 3 -3 2 4 -2 A = and B = 5 1 3 -1 3 2 -2 -1 Given the following descriptions, determine the following elementary matrices and their inverses. a. The elementary matrix E, multiplies the first row of A by 1/4. E 1 b. The elementary matrix E, multiplies the second row of A by -4. E2 ‚E, c. The elementary matrix Ez switches the first and second rows of A E3 E d. The elementary matrix E, adds 3 times the first row of A to the second row of A. 1 E4
e. The elementary matrix E, multiplies the second row of B by 1/6.
Es
E,
f. The elementary matrix Eg multiplies the third row of B by -4.
1
E
Es
g. The elementary matrix E, switches the first and third rows of B.
E
E,
h. The elementary matrix Eg adds 3 times the third row of B to the second row of B.
Es
Transcribed Image Text:e. The elementary matrix E, multiplies the second row of B by 1/6. Es E, f. The elementary matrix Eg multiplies the third row of B by -4. 1 E Es g. The elementary matrix E, switches the first and third rows of B. E E, h. The elementary matrix Eg adds 3 times the third row of B to the second row of B. Es
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