Question

If A=[2 -0.1] and A inverse = [1/2 a] then (a+b) equals


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Answer 1

Answer:

erse Matrices

Suppose A is a square matrix. We look for an “inverse matrix” A-

1 of the same size, such

that A-

1 times A equals I . Whatever A does, A-

1 undoes. Their product is the identity

matrix—which does nothing to a vector, so A-

1Ax D x. But A-

1 might not exist.

What a matrix mostly does is to multiply a vector x. Multiplying Ax D b by A-

1

gives A-

1Ax D A-

1b. This is x D A-

1b. The product A-

1A is like multiplying by

a number and then dividing by that number. A number has an inverse if it is not zero—

matrices are more complicated and more interesting. The matrix A-

1 is called “A inverse.”

DEFINITION The matrix A is invertible if there exists a matrix A-

1 such that

A-

1A D I and AA-

1 D I: