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Find the Inverse of a Matrix (Calculate Inverse Matrix)

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Find the Inverse of a Matrix (Calculate Inverse Matrix)

Here we discuss how to find the inverse of a matrix. In order to do this, we perform the calculation and arrive at what we call the inverse matrix, which is a matrix, when multiplied by the original matrix, yields a matrix with diagonal 1's. This is called the multiplicative inverse. More Lessons: http://www.MathAndScience.com Twitter: https ...

39.8K viewsFeb 2, 2023

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4. (9 points) Give examples of A and B such that(a) A B is not invertible although A and B are invertible.(b) A B is invertible although A and B are not invertible(c) All of A, B and A B are invertible.(d) In the last case, show that B^-1 A^-1 is also invertible and find a formula for its inverse.(Hint: Check this out A^-1(A B)B^-1)

4. (9 points) Give examples of A and B such that(a) A B is not invertible although A and B are invertible.(b) A B is invertible although A and B are not invertible(c) All of A, B and A B are invertible.(d) In the last case, show that B^-1 A^-1 is also invertible and find a formula for its inverse.(Hint: Check this out A^-1(A B)B^-1)

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