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Chapter 10: Q84. (page 530)

Find the inverse of the matrix
$[\begin{matrix} 2 & 4 \\ 5 & 10 \end{matrix}]$
if it exists.

Short Answer

Expert verified

The inverse of the given matrix

$[\begin{matrix} 2 & 4 \\ 5 & 10 \end{matrix}]$

does not exist.

Step by step solution

01

Step 1. Write down the given equation.

The given matrix is say

$P = [\begin{matrix} 2 & 4 \\ 5 & 10 \end{matrix}]$

.

02

Step 2. Concept used.

The inverse of the matrix $A = [\begin{matrix} a & b \\ c & d \end{matrix}]$

exits if $|A| 鈮� 0$ . And inverse of $A = [\begin{matrix} a & b \\ c & d \end{matrix}]$

is given by the formula:

$A^{鈭� 1} = \frac{1}{|A|} [\begin{matrix} d & 鈭� b \\ 鈭� c & a \end{matrix}]$ where $|A| 鈮� 0$

03

Step 3. Evaluating inverse of given matrix.

The inverse of the matrix is evaluated as:

$\begin{array}{l} P = [\begin{matrix} 2 & 4 \\ 5 & 10 \end{matrix}] .... (Given) \\ |P| = 20 鈭� 20 \\ = 0 \end{array}$

Since, $|P| = 0$ . Therefore, the inverse of the matrix

role="math" localid="1648235380892" $[\begin{matrix} 2 & 4 \\ 5 & 10 \end{matrix}]$ does not exist.

04

Step 4. Conclusion.

The inverse of the given matrix $[\begin{matrix} 2 & 4 \\ 5 & 10 \end{matrix}]$ does not exist.

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