Answered

Find answers to your questions faster and easier with IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

Let A,B, and C be square invertible matrices of the same size. If C has no eigenvalue equal to -1, then (AB + ACB)^-1 is equal to:

a. B^-1 (I + C)^-1*A^-1
b. (I + C)^-1*B^-1*A^-1
c. A^-1B*(I + C)^-1
d. (I + C)^-1*BA^-1

Sagot :

LammettHashidn

AB + ACB = A (B + CB) = A (I + C ) B

Taking the inverse gives

(A (I + C ) B)⁻¹ = B ⁻¹ (I + C )⁻¹ A ⁻¹

so the answer is (A)

Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.