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

Step 1. Write down the given equation.

The given matrix is say

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

Step 2. Concept used.

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

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

is given by the formula:

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

Step 3. Evaluating inverse of given matrix.

The inverse of the matrix is evaluated as:

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

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

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

Step 4. Conclusion.

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

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

Short Answer

Step by step solution

Step 1. Write down the given equation.

Step 2. Concept used.

Step 3. Evaluating inverse of given matrix.

Step 4. Conclusion.

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Find the inverse of the matrix24510if it exists.

Short Answer

Step by step solution

Step 1. Write down the given equation.

Step 2. Concept used.

Step 3. Evaluating inverse of given matrix.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Mechanics Maths

Geometry

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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