Chapter 11: Q. 35 (page 756)

In Problems 31– 40, each matrix is non singular. Find the inverse of each matrix.
$[\begin{matrix} 2 & 1 \\ a & a \end{matrix}]$

Short Answer

Expert verified

The inverse of the matrix $[\begin{matrix} 2 & 1 \\ a & a \end{matrix}]$ is $[\begin{matrix} 1 & - \frac{1}{a} \\ - 1 & \frac{2}{a} \end{matrix}]$

Step by step solution

Step 1. Given Information

The matrix $[\begin{matrix} 2 & 1 \\ a & a \end{matrix}]$ is non singular.

Step 2. Form the matrix

$[A I_{2}] = [\begin{matrix} 2 & 1 \\ a & a \end{matrix}] [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

Step 3. Transform equation into reduced row echelon form

$R_{1} \to \frac{1}{2} R_{1} R_{2} \to R_{2} - 2 R_{1} = [\begin{matrix} 1 & \frac{1}{2} \\ 0 & \frac{a}{2} \end{matrix}] [\begin{matrix} \frac{1}{2} & 0 \\ - \frac{a}{2} & 1 \end{matrix}] R_{2} \to \frac{2}{a} R_{2} = [\begin{matrix} 1 & \frac{1}{2} \\ 0 & 1 \end{matrix}] [\begin{matrix} \frac{1}{2} & 0 \\ - 1 & \frac{2}{a} \end{matrix}] R_{1} \to R_{1} - \frac{1}{2} R_{2} = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] [\begin{matrix} 1 & - \frac{1}{a} \\ - 1 & \frac{2}{a} \end{matrix}]$

Step 4. Find the inverse

The inverse of Ais $[\begin{matrix} 1 & - \frac{1}{a} \\ - 1 & \frac{2}{a} \end{matrix}]$

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In Problems 31– 40, each matrix is non singular. Find the inverse of each matrix.
$[\begin{matrix} 2 & 1 \\ a & a \end{matrix}]$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Form the matrix

Step 3. Transform equation into reduced row echelon form

Step 4. Find the inverse

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In Problems 31– 40, each matrix is non singular. Find the inverse of each matrix.21aa

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Form the matrix

Step 3. Transform equation into reduced row echelon form

Step 4. Find the inverse

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Probability and Statistics

Geometry

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 31– 40, each matrix is non singular. Find the inverse of each matrix.
$[\begin{matrix} 2 & 1 \\ a & a \end{matrix}]$