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Linear Algebra With Applications
Found in: Page 308
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

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

Therefore, the given condition is true.

See the step by step solution

Step by Step Solution

 Step 1: Matrix Definition. 

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

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 “ m by n ” matrix, written “ m×n .”

Step 2: Given. 

Given Matrix,


Step 3: To check whether the given condition is true or false.

We compute,


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

Therefore, the given condition is true.

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