Question

A. Write each linear system as a matrix equation in the form $A X=B$ B. Solve the system using the inverse that is given for the coefficient matrix. $$ \left\{\begin{aligned} w-x+2 y &=-3 \\ x-y+z &=4 \\ -w+x-y+2 z &=2 \\ -x+y-2 z &=-4 \end{aligned}\right. $$

Name: Problem 41, Chapter 9: Algebra and Trigonometry
Uploaded: 2020-06-10T13:32:13-08:00
Duration: 4 min 30 s
Channel: Ankit Gupta
Description: A. Write each linear system as a matrix equation in the form A X=B B. Solve the system using the inverse that is given for the coefficient matrix. { w-x+2 y =-3 x-y+z =4 -w+x-y+2 z =2 -x+y-2 z =-4 .

   A. Write each linear system as a matrix equation in the form $A X=B$
B. Solve the system using the inverse that is given for the coefficient matrix.
$$
\left\{\begin{aligned}
w-x+2 y &=-3 \\
x-y+z &=4 \\
-w+x-y+2 z &=2 \\
-x+y-2 z &=-4
\end{aligned}\right.
$$

Algebra and Trigonometry

Robert Blitzer 6th Edition

Chapter 9, Problem 41

Instant Answer

Solved by Expert Ankit Gupta

06/10/2020

Step 1

The coefficient matrix A is formed by the coefficients of the variables w, x, y, and z in each equation. The variable matrix X contains the variables w, x, y, and z. The constant matrix B contains the constants on the right side of each equation. So, we Show more…

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A. Write each linear system as a matrix equation in the form $A X=B$ B. Solve the system using the inverse that is given for the coefficient matrix. $$ \left\{\begin{aligned} w-x+2 y &=-3 \\ x-y+z &=4 \\ -w+x-y+2 z &=2 \\ -x+y-2 z &=-4 \end{aligned}\right. $$

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Key Concepts

Matrix Equation Representation

This concept involves expressing a system of linear equations in the compact form AX = B, where A is the coefficient matrix containing the coefficients of the variables, X is the vector of unknowns, and B is the vector of constants. This formulation provides a convenient and systematic way to analyze and solve multiple simultaneous linear equations using matrix operations.

Solving Linear Systems Using Matrix Inverses

When the coefficient matrix A is invertible, the system AX = B can be solved by multiplying both sides of the equation by the inverse of A. This yields the solution X = A?¹B. This method highlights the importance of matrix invertibility and provides a straightforward computational approach for finding the unique solution to a system of linear equations.

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