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Chapter 9: Problem 81

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used matrix multiplication to represent a system of linear equations.

Short Answer

Expert verified
The statement makes sense. Matrix multiplication is often used to represent systems of linear equations.

Step by step solution

01

Understanding the relationship between matrices and linear systems

In linear algebra, a system of linear equations can be represented in matrix form. If given a system of equations, one can write the system in terms of a coefficient matrix \(A\), a variable matrix \(X\) and a constant matrix \(B\). In this form, the system can be represented as \(AX = B\). The operation involved in this representation is matrix multiplication.
02

Evaluating the Statement

The given statement 'I used matrix multiplication to represent a system of linear equations' is an accurate representation of the use of matrices to depict a system of linear equations. This is a fundamental concept in linear algebra, and shows the robustness of matrix operations in solving systems of linear equations.

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Most popular questions from this chapter

The figure shows the letter \(L\) in a rectangular coordinate system. The figure can be represented by the matrix $$ B=\left[\begin{array}{llllll} {0} & {3} & {3} & {1} & {1} & {0} \\ {0} & {0} & {1} & {1} & {5} & {5} \end{array}\right] $$ Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The L is completed by connecting the last point in the matrix, (0,5), to the starting point, (0,0) . Use these ideas to solve Exercises 53-60. a. If \(A=\left[\begin{array}{rr}{-1} & {0} \\ {0} & {1}\end{array}\right],\) find \(A B\). b. Graph the object represented by matrix \(A B .\) What effect does the matrix multiplication have on the letter \(\mathrm{L}\) represented by matrix \(B ?\)

Find (if possible) the following matrices: a. \(A B\) b. \(B A\) $$ A=\left[\begin{array}{llll} {1} & {2} & {3} & {4} \end{array}\right], \quad B=\left[\begin{array}{l} {1} \\ {2} \\ {3} \\ {4} \end{array}\right] $$

Describe how to subtract matrices.

Find (if possible) the following matrices: a. \(A B\) b. \(B A\) $$ A=\left[\begin{array}{rrrr} {2} & {-3} & {1} & {-1} \\ {1} & {1} & {-2} & {1} \end{array}\right], \quad B=\left[\begin{array}{rr} {1} & {2} \\ {-1} & {1} \\ {5} & {4} \\ {10} & {5} \end{array}\right] $$

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. $$ 3 X+A=B $$
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