Chapter 4: Q46. (page 201)

Which matrix does not have an inverse?
A $[\begin{matrix} 5 & 3 \\ 2 & 4 \end{matrix}]$ B $[\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$ C localid="1647955428480" $[\begin{matrix} - 3 & - 3 \\ 6 & - 6 \end{matrix}]$ D $[\begin{matrix} - 10 & - 5 \\ 8 & 4 \end{matrix}]$

Short Answer

Expert verified

The matrix that does not have an inverse is: $D [\begin{matrix} - 10 & - 5 \\ 8 & 4 \end{matrix}]$

Step by step solution

- Description of step.

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

A square matrix $A$ have its inverse if $|A| \neq 0$ .

- Find the determinant of the given matrices.

The determinant of the matrix $[\begin{matrix} 5 & 3 \\ 2 & 4 \end{matrix}]$ is:

$\begin{matrix} |\begin{matrix} 5 & 3 \\ 2 & 4 \end{matrix}| = (5) (4) - (2) (3) \\ = 20 - 6 \\ = 14 \end{matrix}$

The determinant of the matrixlocalid="1647955522080" $[\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$ is:

$\begin{matrix} |\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}| = (1) (1) - (2) (2) \\ = 1 - 4 \\ = - 3 \end{matrix}$

The determinant of the matrix localid="1647955530560" $[\begin{matrix} - 3 & - 3 \\ 6 & - 6 \end{matrix}]$ is:

$\begin{matrix} |\begin{matrix} - 3 & - 3 \\ 6 & - 6 \end{matrix}| = (- 3) (- 6) - (6) (- 3) \\ = 18 - (- 18) \\ = 18 + 18 \\ = 36 \end{matrix}$

The determinant of the matrix localid="1647955553284" $[\begin{matrix} - 10 & - 5 \\ 8 & 4 \end{matrix}]$ is:

$\begin{matrix} |\begin{matrix} - 10 & - 5 \\ 8 & 4 \end{matrix}| = (- 10) (4) - (8) (- 5) \\ = - 40 - (- 40) \\ = - 40 + 40 \\ = 0 \end{matrix}$

As the determinant of the matrix

localid="1647955567000" $[\begin{matrix} - 10 & - 5 \\ 8 & 4 \end{matrix}]$ is equal to zero, therefore the inverse of the matrix localid="1647955576857" $[\begin{matrix} - 10 & - 5 \\ 8 & 4 \end{matrix}]$ does not exist.

- Description of step.

The matrix that does not have an inverse is $[\begin{matrix} - 10 & - 5 \\ 8 & 4 \end{matrix}]$ .

Therefore, the option D is correct.

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Which matrix does not have an inverse?
A $[\begin{matrix} 5 & 3 \\ 2 & 4 \end{matrix}]$ B $[\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$ C localid="1647955428480" $[\begin{matrix} - 3 & - 3 \\ 6 & - 6 \end{matrix}]$ D $[\begin{matrix} - 10 & - 5 \\ 8 & 4 \end{matrix}]$

Short Answer

Step by step solution

- Description of step.

- Find the determinant of the given matrices.

- Description of step.

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Which matrix does not have an inverse?A 5324 B1221 C localid="1647955428480" -3-36-6 D-10-584

Short Answer

Step by step solution

­- Description of step.

­- Find the determinant of the given matrices.

­- Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Calculus

Theoretical and Mathematical Physics

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Which matrix does not have an inverse?
A $[\begin{matrix} 5 & 3 \\ 2 & 4 \end{matrix}]$ B $[\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$ C localid="1647955428480" $[\begin{matrix} - 3 & - 3 \\ 6 & - 6 \end{matrix}]$ D $[\begin{matrix} - 10 & - 5 \\ 8 & 4 \end{matrix}]$

- Description of step.

- Find the determinant of the given matrices.

- Description of step.