Write the matrix equation as a system of equations. [ 1 0 -3 2 -1 3 -2 3

Name: Problem 48, Chapter 7: Precalculus: Graphical, Numerical, Algebraic
Uploaded: 2020-02-09T04:43:50-08:00
Duration: 1 min 26 s
Channel: Heather Zimmers
Description: Write the matrix equation as a system of equations. [ 1 0 -3 2 -1 3 -2 3 -4 ][ x y z ]=[ 3 -1 2 ]

step 1 Here we have a matrix equation that represents a system of three equations. And the first matrix

Question

Write the matrix equation as a system of equations. $$\left[\begin{array}{rrr}{1} & {0} & {-3} \\ {2} & {-1} & {3} \\ {-2} & {3} & {-4}\end{array}\right]\left[\begin{array}{l}{x} \\ {y} \\ {z}\end{array}\right]=\left[\begin{array}{r}{3} \\ {-1} \\ {2}\end{array}\right]$$

   Write the matrix equation as a system of equations.
$$\left[\begin{array}{rrr}{1} & {0} & {-3} \\ {2} & {-1} & {3} \\ {-2} & {3} & {-4}\end{array}\right]\left[\begin{array}{l}{x} \\ {y} \\ {z}\end{array}\right]=\left[\begin{array}{r}{3} \\ {-1} \\ {2}\end{array}\right]$$

Precalculus: Graphical, Numerical, Algebraic

Franklin D.… 8th Edition

Chapter 7, Problem 48

Instant Answer

Solved by Expert Heather Zimmers

02/09/2020

Step 1

The first matrix (Matrix A) contains the coefficients of the variables in the equations, the second matrix (Matrix X) contains the variables, and the third matrix (Matrix B) contains the constants. Show more…

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Write the matrix equation as a system of equations. $$\left[\begin{array}{rrr}{1} & {0} & {-3} \\ {2} & {-1} & {3} \\ {-2} & {3} & {-4}\end{array}\right]\left[\begin{array}{l}{x} \\ {y} \\ {z}\end{array}\right]=\left[\begin{array}{r}{3} \\ {-1} \\ {2}\end{array}\right]$$

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Key Concepts

System of Linear Equations

A system of linear equations consists of several equations that involve the same set of variables. By representing the coefficients in a matrix and the variables in a vector, the system can be expressed in a compact matrix equation form. This perspective is used to simplify the process of solving multiple equations simultaneously and provides a framework for applying various algebraic methods.

Matrix Multiplication

Matrix multiplication is a process of combining a matrix and a vector (or another matrix) to produce a new vector (or matrix). Each entry in the resulting vector is computed by taking the dot product of a row of the matrix with the column vector, which is fundamental to representing and solving systems of linear equations in compact form.

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