Exercise 2.1
Q #: 10
Let
A = and B =
What value(s) of k if any will make AB = BA?
Solution:
AB =
=
=
BA =
=
=
For AB = BA
=
12-4k = -24
k = 9
Also 15 – 5k= -30
k = 9
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Exercise Solutions for Matrix Invertibility, Exercises of Linear Algebra
The solutions to exercise 2.1 and exercise 2.2 from a linear algebra course, focusing on matrix invertibility and related concepts. It covers topics such as finding values of k that make the product of two matrices equal to its transpose, determining if a product of invertible matrices is invertible, and justifying statements about invertible matrices.
Typology: Exercises
2011/2012
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Exercise 2.
Q #: 10
Let
A = and B =
What value(s) of k if any will make AB = BA? Solution:
AB =
= BA = = =
For AB = BA
=
12-4k = - k = 9 Also 15 – 5k= - k = 9
docsity.com
Exercise 2.
Q #: 10
Mark each statement True or False. Justify each answer. (a): Statement: A product of invertible n n matrices is invertible, and the inverse of the product is the product of their inverses. Answer: False. The phrase “in the reverse order” is missing. (b): Statement: If A is invertible then the inverse of A-1^ is A itself. Answer: True. Theorem 6(a). (c):
Statement: If A = and ad = bc, then A is non invertible.
Answer: True. Because then | A | = 0. (d): Statement: If A can be row reduced to the identity matrix, then A must be invertible. Answer: True. Theorem 7. (e): Statement: If A is invertible, then elementary row operations that reduce A to the identity In also reduce A-1^ to In. Answer: False. They transform In to A-1 , not A-1^ to In.