Chapter 5: Q69. (page 228)

Find the inverse of the matrix $[\begin{matrix} \begin{matrix} 4 & 3 \\ 2 & 1 \end{matrix} \end{matrix}]$ if it exists.

Short Answer

Expert verified

The inverse of the given matrix is $\frac{1}{2} [\begin{matrix} - 1 & 3 \\ 2 & - 4 \end{matrix}]$ .

Step by step solution

Step 1. Write down the given matrix.

The given matrix is say, $P = [\begin{matrix} 4 & 3 \\ 2 & 1 \end{matrix}]$ .

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{matrix} P = [\begin{matrix} 4 & 3 \\ 2 & 1 \end{matrix}] .... (Given) \\ | P | = 4 - 6 \\ = - 2 \end{matrix}

Now evaluating inverse of $P = [\begin{matrix} 4 & 3 \\ 2 & 1 \end{matrix}]$ by the formula stated above.

$\begin{matrix} P^{- 1} = \frac{1}{- 2} [\begin{matrix} 1 & - 3 \\ - 2 & 4 \end{matrix}] \\ = \frac{1}{2} [\begin{matrix} - 1 & 3 \\ 2 & - 4 \end{matrix}] \end{matrix}$

Step 4. Conclusion.

Hence the inverse of the given matrix is $\frac{1}{2} [\begin{matrix} - 1 & 3 \\ 2 & - 4 \end{matrix}]$ .

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Find the inverse of the matrix $[\begin{matrix} \begin{matrix} 4 & 3 \\ 2 & 1 \end{matrix} \end{matrix}]$ if it exists.

Short Answer

Step by step solution

Step 1. Write down the given matrix.

Step 2. Concept used.

Step 3. Evaluating inverse of given matrix.

Step 4. Conclusion.

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Find the inverse of the matrix4321 if it exists.

Short Answer

Step by step solution

Step 1. Write down the given matrix.

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

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Find the inverse of the matrix $[\begin{matrix} \begin{matrix} 4 & 3 \\ 2 & 1 \end{matrix} \end{matrix}]$ if it exists.