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Chapter 6: Q11E (page 308)

The matrix [k214k-1-2111] is invertible for all positive constantsk.

Short Answer

Expert verified

Therefore, the given condition is true.

Step by step solution

01

 Step 1: Matrix Definition. 

Matrix is aset of numbers arranged in rows and columns so as to form a rectangulararray.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an 鈥� m by n 鈥� matrix, written 鈥�m脳n .鈥�

02

Given. 

Given Matrix,

[k214k-1-2111]

03

To check whether the given condition is true or false.

We compute,

detA=-k2-2+4k+4+2k2-kdetA=k2+3k+2

which turns out to be 0 if and only if k=-2or k=-1, so for all positive constants k, the matrix is regular.

Therefore, the given condition is true.

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