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Chapter 2: Q23E (page 108)

TRUE OR FALSE?

There exists a matrix A such that A(1111)=(1212) .

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Invertible matrix

The matrix is said to be invertible, if and only if the reduced row echelon form of the matrix has nonzero diagonal elements and for the second-order matrix, the determinant of the matrix should be nonzero.

02

Compute the matrix

Consider the condition.

A=1111=1212鈬�A=12121111-1

If the determinant of the matrix is zero, then, this inverse does not exist.

As det1111=0 thus, the inverse does not exist.

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