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Chapter 2: Q12E (page 108)

TRUE OR FALSE?

There exists a real number Ksuch that the matrix[k-1-2-4k-3]fails to be invertible.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Compute the determinant of the matrix.

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

Consider the matrix.

k-1-2-4k-3

The determinant of the matrix is,

detk-1-2-4k-3=(k-1)(k-1)-(-2)(-4)=k2-4k-5

As the matrix fails to be invertible, so,

0=k2-4k-5鈬�(k-5)(k+1)=0鈭�k=-1,5

There exists the real number.

02

Find the value of unknown

As the matrix fails to be invertible, so,

0=k2-4k-5鈬�(k-5)(k+1)=0鈭�k=-1,5

There exists the real number.

Hence, the given statement is true.

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