A = E₁ = 5 2 -1 4 E2 and B = -5 -3 -4 -24 -5 -5 1 Given the following descriptions, determine the following elementary matrices and their inverses. a. The elementary matrix E₁ multiplies the first row of A by 1/5. 2 E-1 b. The elementary matrix E2 multiplies the second row of A by -3. - ‚E₂¹ = c. The elementary matrix E3 switches the first and second rows of A.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 47RE
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Question
A =
E₁
E2
Given the following descriptions, determine the following elementary matrices and their inverses.
E3
a. The elementary matrix ₁ multiplies the first row of A by 1/5.
Е₁
=
E5
b. The elementary matrix E2 multiplies the second row of A by -3.
=
E6
E
=
5 2
c. The elementary matrix E3 switches the first and second rows of A.
Es
-1 4
=
and B =
-5 -3 -4
-2 4-5
d. The elementary matrix E4 adds 7 times the first row of A to the second row of A.
3
||
-5 1 2
=
=
‚E¹
e. The elementary matrix 5 multiplies the second row of B by 1/5.
-1
f. The elementary matrix 6 multiplies the third row of B by -3.
B
g. The elementary matrix E switches the first and third rows of B.
‚,E¹
1
E¹
E5¹
1
E6¹
-1
‚E-¹
h. The elementary matrix Eg adds 3 times the third row of B to the second row of B.
Eg
=
1
=
Transcribed Image Text:A = E₁ E2 Given the following descriptions, determine the following elementary matrices and their inverses. E3 a. The elementary matrix ₁ multiplies the first row of A by 1/5. Е₁ = E5 b. The elementary matrix E2 multiplies the second row of A by -3. = E6 E = 5 2 c. The elementary matrix E3 switches the first and second rows of A. Es -1 4 = and B = -5 -3 -4 -2 4-5 d. The elementary matrix E4 adds 7 times the first row of A to the second row of A. 3 || -5 1 2 = = ‚E¹ e. The elementary matrix 5 multiplies the second row of B by 1/5. -1 f. The elementary matrix 6 multiplies the third row of B by -3. B g. The elementary matrix E switches the first and third rows of B. ‚,E¹ 1 E¹ E5¹ 1 E6¹ -1 ‚E-¹ h. The elementary matrix Eg adds 3 times the third row of B to the second row of B. Eg = 1 =
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