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Chapter 2: Q 38E (page 98)

Question:Find A-1 for A=(1k0鈭�1).

Short Answer

Expert verified

The inverse matrix is,A鈭�1=1k0鈭�1.

Step by step solution

01

Consider the matrix

Consider the matrix

A=1k0鈭�1鈥�

The matrix is said to be invertible if and only if the determinant of the matrix is nonzero.

The inverse of the matrix is,

(abcd)鈭�1=1ad鈭�bc(d鈭�b鈭�ca)

Where,det(abcd)=ad鈭�bc.

02

Compute the inverse of the matrix.

The inverse of the matrix is,

A鈭�1=1k0鈭�1鈭�1=11脳(鈭�1)鈭�k脳0鈭�1鈭�k01=1鈭�1鈭�1鈭�k01鈭�A鈭�1=1k0鈭�1

Hence, A鈭�1=1k0鈭�1 is the inverse matrix of A=1k0鈭�1.

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Most popular questions from this chapter

If A is any transition matrix and B is any positive transition matrix, then AB must be a positive transition matrix.

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You are told that T is a linear transformation. (This will be shown in the next section.) Find the matrix of T .

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