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4. A = [ 5 7 5 ²]. b = = ['₁ 5 12 17

4. A = [ 5 7 5 ²]. b = = ['₁ 5 12 17

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question

First, apply the formulas in (9) to find A^-1. Then use A^-1 to solve the system Ax=b.

**THEOREM 2: Inverses of 2 x 2 Matrices** The 2 x 2 matrix \[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \] is invertible if and only if \( ad - bc \neq 0 \), in which case \[ A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}. \]
Transcribed Image Text:**THEOREM 2: Inverses of 2 x 2 Matrices** The 2 x 2 matrix \[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \] is invertible if and only if \( ad - bc \neq 0 \), in which case \[ A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}. \]
In this image, we have two matrices represented. Matrix **A** is a 2x2 matrix: \[ A = \begin{bmatrix} 5 & 12 \\ 7 & 17 \end{bmatrix} \] Matrix **b** is a 2x1 matrix (also known as a column vector): \[ b = \begin{bmatrix} 5 \\ 5 \end{bmatrix} \] This type of representation is typically used in linear algebra to solve systems of equations or perform matrix operations such as multiplication, addition, or finding inverses.
Transcribed Image Text:In this image, we have two matrices represented. Matrix **A** is a 2x2 matrix: \[ A = \begin{bmatrix} 5 & 12 \\ 7 & 17 \end{bmatrix} \] Matrix **b** is a 2x1 matrix (also known as a column vector): \[ b = \begin{bmatrix} 5 \\ 5 \end{bmatrix} \] This type of representation is typically used in linear algebra to solve systems of equations or perform matrix operations such as multiplication, addition, or finding inverses.
Expert Solution
Step 1: Given value of A and b

Given, A equals open square brackets table row 5 12 row 7 17 end table close square brackets comma space space b equals open square brackets table row 5 row 5 end table close square brackets

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