Chapter 4: Q3. (page 198)

Create a square matrix that does not have an inverse.

Short Answer

Expert verified

The square matrix that does not have an inverse is: $[\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}]$ .

Step by step solution

- Description of step.

A square matrix is a matrix which has same number of rows and columns.

- Description of step.

A square matrix A does not have its inverse if $|A| = 0$ .

Therefore, to create a square matrix that does not have its inverse, create a matrix which is having it’s determinant as 0.

- Description of step.

Consider the matrix $A$ as localid="1648139074688" $[\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}]$ .

Notice that:

$\begin{matrix} |\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}| = (1) (4) - (2) (2) \\ = 4 - 4 \\ = 0 \end{matrix}$

As, $|A| = 0$ , therefore the matrix $A$ will not have an inverse.

Therefore, the square matrix that does not have an inverse is: localid="1648139087180" $[\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}]$ .

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Create a square matrix that does not have an inverse.

Short Answer

Step by step solution

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Create a square matrix that does not have an inverse.

Short Answer

Step by step solution

­- Description of step.

­- Description of step.

­- Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

- Description of step.

- Description of step.

- Description of step.