3. Verify that the following statement is true for these matrices: (XY)-1 = Y-!X-!. A suggestion: Use the previous result to simplify your calcula-

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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Question
Part 3
1. Calculate the determinate of matrices X and Y. Use row addition
and subtraction where it makes your calculations easier.
2. Verify that the following statement is true for these matrices:
det (XY) = det(X) det(Y).
3. Verify that the following statement is true for these matrices:
(XY)-1 = Y-!x-!.
A suggestion: Use the previous result to simplify your calcula-
tions.
4. Prove that the statement
(XY)-1 = Y-lXx-1
is true for any two square matrices, where their inverses exist.
5. Let T be an unknown 3 by 2 matrix, where
XT = Y Z.
Solve this matrix equation for T, where possible.
Transcribed Image Text:1. Calculate the determinate of matrices X and Y. Use row addition and subtraction where it makes your calculations easier. 2. Verify that the following statement is true for these matrices: det (XY) = det(X) det(Y). 3. Verify that the following statement is true for these matrices: (XY)-1 = Y-!x-!. A suggestion: Use the previous result to simplify your calcula- tions. 4. Prove that the statement (XY)-1 = Y-lXx-1 is true for any two square matrices, where their inverses exist. 5. Let T be an unknown 3 by 2 matrix, where XT = Y Z. Solve this matrix equation for T, where possible.
-3
-7
B =
-5
1
-8
-2
-3
B Question 2
-(:):( )
7
6.
Z =
9.
20
21
22
-5
8.
23
Y =
-2
-5
1
24
-8
-2
-3
25
26
27
Worksheet 1
Worksheet 2
+,
Ready
Transcribed Image Text:-3 -7 B = -5 1 -8 -2 -3 B Question 2 -(:):( ) 7 6. Z = 9. 20 21 22 -5 8. 23 Y = -2 -5 1 24 -8 -2 -3 25 26 27 Worksheet 1 Worksheet 2 +, Ready
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