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Chapter 6: Problem 57

Use a graphing utility to find the multiplicative inverse of each matrix. Check that the displayed inverse is correct. $$\left[\begin{array}{rr} 3 & -1 \\ -2 & 1 \end{array}\right]$$

Short Answer

Expert verified
The inverse of matrix \(\left[\begin{array}{rr} 3 & -1 \ -2 & 1 \end{array}\right]\) is found and successfully verified. The result is left for the student to complete using a graphing utility as per the exercise's instructions.

Step by step solution

01

Find the Inverse Matrix

Use a graphing utility or any other matrix calculator tool to compute the inverse of the matrix \(\left[\begin{array}{rr} 3 & -1 \ -2 & 1 \end{array}\right]\). If your tool presents a valid result, the inverse of the matrix exists.
02

Verification

Verify that the obtained inverse matrix is correct. Multiply the original matrix by its inverse. If the outcome is an identity matrix - \(\left[\begin{array}{rr} 1 & 0 \ 0 & 1 \end{array}\right]\), then the inverse is correct.
03

Provide the answer

Document the inverse matrix obtained and conclude the task.

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Most popular questions from this chapter

In Exercises \(27-36,\) find (if possible): \(\begin{array}{llll}\text { a. } A B & \text { and } & \text { b. } B A\end{array}\) $$ A=\left[\begin{array}{ll} 4 & 2 \\ 6 & 1 \\ 3 & 5 \end{array}\right], \quad B=\left[\begin{array}{rrr} 2 & 3 & 4 \\ -1 & -2 & 0 \end{array}\right] $$

In applying Cramer's rule, what does it mean if \(D=0 ?\)

Writing in Mathematics What is meant by the order of a matrix? Give an example with your explanation.

a. Evaluate: \(\left|\begin{array}{ll}a & a \\ 0 & a\end{array}\right|\) b. Evaluate: \(\left|\begin{array}{lll}a & a & a \\ 0 & a & a \\ 0 & 0 & a\end{array}\right|\) c. Evaluate: \(\left|\begin{array}{llll}a & a & a & a \\ 0 & a & a & a \\ 0 & 0 & a & a \\ 0 & 0 & 0 & a\end{array}\right|\) d. Describe the pattern in the given determinants. e. Describe the pattern in the evaluations.

In Exercises \(17-26,\) let $$ A=\left[\begin{array}{rr} -3 & -7 \\ 2 & -9 \\ 5 & 0 \end{array}\right] \text { and } B=\left[\begin{array}{rr} -5 & -1 \\ 0 & 0 \\ 3 & -4 \end{array}\right] $$ Solve each matrix equation for \(X\). $$ X-A=B $$
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