Q31. Find the inverse of each matrix,... [FREE SOLUTION]

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Chapter 4: Q31. (page 199)

Find the inverse of each matrix, if it exists.31.
$[\begin{matrix} \frac{3}{10} & \frac{5}{8} \\ \frac{1}{5} & \frac{3}{4} \end{matrix}]$

Short Answer

Expert verified

The inverse of the given matrix is $[\begin{matrix} \frac{15}{2} & - \frac{25}{4} \\ - 2 & 3 \end{matrix}]$

Step by step solution

- Description of step.

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

A square matrixA have its inverse if . $| A | 鈮� 0$

- Find the determinant of the given matrix.

The determinant of the given matrix is:

$\begin{matrix} | \begin{matrix} \frac{3}{10} & \frac{5}{8} \\ \frac{1}{5} & \frac{3}{4} \end{matrix} | = (\frac{3}{10}) (\frac{3}{4}) 鈭� (\frac{1}{5}) (\frac{5}{8}) \\ = \frac{9}{40} 鈭� \frac{5}{40} \\ = \frac{9 鈭� 5}{40} \\ = \frac{4}{40} \\ = \frac{1}{10} \end{matrix}$

As the determinant of the given matrix is not equal to zero, therefore the inverse of the given matrix exists.

- Description of step.

The inverse of $2 脳 2$ matrix $A = [\begin{matrix} a & b \\ c & d \end{matrix}]$ is given by $A^{鈭� 1} = \frac{1}{a d 鈭� b c} [\begin{matrix} d & 鈭� b \\ 鈭� c & a \end{matrix}]$ and . $a d 鈭� b c 鈮� 0$

- Description of step.

The inverse of the given matrix is given by:

$\begin{matrix} \frac{1}{(\frac{3}{10}) (\frac{3}{4}) 鈭� (\frac{1}{5}) (\frac{5}{8})} [\begin{matrix} \frac{3}{4} & 鈭� (\frac{5}{8}) \\ 鈭� (\frac{1}{5}) & \frac{3}{10} \end{matrix}] = \frac{1}{\frac{9}{40} 鈭� \frac{5}{40}} [\begin{matrix} \frac{3}{4} & 鈭� \frac{5}{8} \\ 鈭� \frac{1}{5} & \frac{3}{10} \end{matrix}] \\ = \frac{1}{\frac{4}{40}} [\begin{matrix} \frac{3}{4} & 鈭� \frac{5}{8} \\ 鈭� \frac{1}{5} & \frac{3}{10} \end{matrix}] \\ = \frac{1}{\frac{1}{10}} [\begin{matrix} \frac{3}{4} & 鈭� \frac{5}{8} \\ 鈭� \frac{1}{5} & \frac{3}{10} \end{matrix}] \\ = 10 [\begin{matrix} \frac{3}{4} & 鈭� \frac{5}{8} \\ 鈭� \frac{1}{5} & \frac{3}{10} \end{matrix}] \\ = [\begin{matrix} \frac{30}{4} & 鈭� \frac{50}{8} \\ 鈭� \frac{10}{5} & \frac{30}{10} \end{matrix}] \\ = [\begin{matrix} \frac{15}{2} & 鈭� \frac{25}{4} \\ 鈭� 2 & 3 \end{matrix}] \end{matrix}$

Therefore, the inverse of the given matrix is $[\begin{matrix} \frac{15}{2} & 鈭� \frac{25}{4} \\ 鈭� 2 & 3 \end{matrix}]$

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91影视

Find the inverse of each matrix, if it exists.31.
$[\begin{matrix} \frac{3}{10} & \frac{5}{8} \\ \frac{1}{5} & \frac{3}{4} \end{matrix}]$

Short Answer

Step by step solution

- Description of step.

- Find the determinant of the given matrix.

- Description of step.

- Description of step.

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91影视

Find the inverse of each matrix, if it exists.31.[310581534]

Short Answer

Step by step solution

­- Description of step.

­- Find the determinant of the given matrix.

­- Description of step.

­- Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Decision Maths

Mechanics Maths

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the inverse of each matrix, if it exists.31.
$[\begin{matrix} \frac{3}{10} & \frac{5}{8} \\ \frac{1}{5} & \frac{3}{4} \end{matrix}]$

- Description of step.

- Find the determinant of the given matrix.

- Description of step.

- Description of step.