Suppose that: -2 -2 2 -2 -5 A = and B = -3 -2 -1 -2 1 -3 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, b. The elementary matrix E, multiplies the second row of A by –2. E2 . E, c. The elementary matrix E3 switches the first and second rows of A. E3 E,

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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Suppose that:
-2 -2
-2 -5
A =
and B =
-3 -2
-1
-2
1
-3
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.
E1
E,
b. The elementary matrix E, multiplies the second row of A by -2.
E2
E,
c. The elementary matrix E3 switches the first and second rows of A.
E3
Eg
d. The elementary matrix E, adds 7 times the first row of A to the second row of A.
E4 =
e. The elementary matrix E, multiplies the second row of B by 1/4.
E, =
E,' =
2.
Transcribed Image Text:Suppose that: -2 -2 -2 -5 A = and B = -3 -2 -1 -2 1 -3 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. E1 E, b. The elementary matrix E, multiplies the second row of A by -2. E2 E, c. The elementary matrix E3 switches the first and second rows of A. E3 Eg d. The elementary matrix E, adds 7 times the first row of A to the second row of A. E4 = e. The elementary matrix E, multiplies the second row of B by 1/4. E, = E,' = 2.
f. The elementary matrix E, multiplies the third row of B by -5.
E6
E, 1
g. The elementary matrix E, switches the first and third rows of B.
E,'
h. The elementary matrix Eg adds 7 times the third row of B to the second row of B.
Eg =
E,1
Transcribed Image Text:f. The elementary matrix E, multiplies the third row of B by -5. E6 E, 1 g. The elementary matrix E, switches the first and third rows of B. E,' h. The elementary matrix Eg adds 7 times the third row of B to the second row of B. Eg = E,1
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