**Finding the Inverse of a Matrix****Problem Statement:**Find the inverse of the matrix.\[ \begin{bmatrix} 5 & 5 \\ -6 & -5 \end{bmatrix} \]**Instructions:**Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.**Options:**- **Option A:**\[ \left( \begin{bmatrix} 5 & 5 \\ -6 & -5 \end{bmatrix} \right)^{-1} = \begin{bmatrix}\quad \boxed{} & \quad \boxed{} \\[6pt]\quad \boxed{} & \quad \boxed{}\end{bmatrix} \](Simplify your answers.)- **Option B:**The matrix is not invertible.**Explanation:**To declare the matrix invertible, calculate its determinant. If the determinant is non-zero, the matrix is invertible, and we can proceed to find its inverse. If the determinant is zero, the matrix is not invertible.**Graph/Diagram Analysis:**The given matrix is \[ \begin{bmatrix} 5 & 5 \\ -6 & -5 \end{bmatrix} \]. Options provided include selecting whether the matrix is invertible and if so, computing the values of its inverse entries. To solve for the inverse when the determinant is non-zero, use the formula for the inverse of a 2x2 matrix:\[ \text{If } A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}, \text{ then } A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}.\] The determinants, intermediate steps, and verification should be calculated to finalize the correct answer.**Further Discussion:**Consider working through the determinant calculation and necessary algebraic steps to verify the correct choice between options A or B. Ensure to simplify answers in option A for correct entries if the matrix is indeed invertible.

Answered: Image /qna-images/answer/5d124512-ab09-4290-94be-0f10e87dd9f6.jpg

Find the inverse of the matrix. 5 5 -6 -5 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. 5 5 -6 -5 (Simplify your answers.) O B. The matrix is not invertible.

Find the inverse of the matrix. 5 5 -6 -5 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. 5 5 -6 -5 (Simplify your answers.) O B. The matrix is not invertible.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Find the inverse of the given matrix. 4 A= 4 Select the correct choice below and, if necessary, fill…

Q: If the given matrix is invertible, find its inverse. 3 3 A= 2 7 Find the inverse. Select the correct…

A: 1) Given, A=3327 find 2×2 matrix inverse according to the formula: A-1=1detAd-b-ca ∵A=abcd

Q: Perform the addition, if possible. 8 −5 1 0 + −9 5 4 −3 Is the addition possible? Yes…

A: A=8-51 0 AND B=[-9 54-3] AS BOTH OF THE MATRIX ARE OF SAME ORDER 2×2 SO,ADDITION IS POSSIBLE…

Q: Find the inverse, if it exists, for the given matrix. -2 -4 -8 Select the correct choice below and,…

A: Given matrix is A=−1−2−4−8. We have to find the inverse of the given matrix A. First we will find…

Q: Find the inverse, if it exists, for the given matrix. -5 - 10 - 3 -6 Select the correct choice below…

Q: Solve for A: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right…

Q: Find the inverse of the given matrix, if it exists. M= 2 -7 7 - 24 Select the correct choice below…

A: M=2-77-24 We have to find the inverse of the matrix.

Q: Find the inverse of the given matrix, if it exists. 1 -2 1 A = 4 -7 3 -2 - 4 Find the inverse.…

Q: H5. Consider the matrix 0 c-[98] C= -1 0 First, show that C² = -I and use this relationship to…

Q: 3. Determine the inverse of the matrix A. 5 3 -4 A = 3 8 -2 -4 -2 7

Q: Determine the size of the matrix. 2 -1 -1 1 -6 2 0 1 -5 -3 -1 1 3 4 0 1 X

Q: Find the inverse of the given matrix, if it exists. 1 -2 1 A = - 2 5 -3 4 -6 ... Find the inverse.…

A: A matrix is said to have an inverse when the matrix is non singular and a matrix is said to be non…

Q: Matrix Arithmetic: Perform the following calculations for A and B. 5A+2B [3 6 01 A = 2 7 9 12 1 31…

Q: A6 Suppose = A - Find an invertible matrix P and a diagonal matrix D so that A of P, a power of D,…

Question

**Finding the Inverse of a Matrix**

**Problem Statement:**
Find the inverse of the matrix.
\[ \begin{bmatrix} 5 & 5 \\ -6 & -5 \end{bmatrix} \]

**Instructions:**
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

**Options:**
- **Option A:**
\[ \left( \begin{bmatrix} 5 & 5 \\ -6 & -5 \end{bmatrix} \right)^{-1} = \begin{bmatrix}
\quad \boxed{} & \quad \boxed{} \\[6pt]
\quad \boxed{} & \quad \boxed{}
\end{bmatrix} \]
(Simplify your answers.)

- **Option B:**
The matrix is not invertible.

**Explanation:**
To declare the matrix invertible, calculate its determinant. If the determinant is non-zero, the matrix is invertible, and we can proceed to find its inverse. If the determinant is zero, the matrix is not invertible.

**Graph/Diagram Analysis:**
The given matrix is \[ \begin{bmatrix} 5 & 5 \\ -6 & -5 \end{bmatrix} \]. Options provided include selecting whether the matrix is invertible and if so, computing the values of its inverse entries. To solve for the inverse when the determinant is non-zero, use the formula for the inverse of a 2x2 matrix:
\[ \text{If } A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}, \text{ then } A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}.\] The determinants, intermediate steps, and verification should be calculated to finalize the correct answer.

**Further Discussion:**
Consider working through the determinant calculation and necessary algebraic steps to verify the correct choice between options A or B. Ensure to simplify answers in option A for correct entries if the matrix is indeed invertible.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inverse of a Matrix$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

6
A = -1 2 3 2 Enter values in the matrix so that the matrix is singular. Click on Show steps if you want more information on singular matrices. 2 2
Find the following matrix product, if it exists. -4 -5 -3 -2 1 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. -2 0 -1-4 3 3 -2 0 -1 -4 3 3 OB. The product does not exist. OA. -4 -5 -3 -2 1 0 n example Get more help - N H (Simplify your answer.) W I Clear all Check answer prt sc delete
Perform the indicated matrix calculation. 3 7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. -5 3 -9 O A. 7 (Type an integer or simplified fraction for each matrix element) O B. The product is undefined.