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Chapter 6: Problem 54

What are equal matrices?

Short Answer

Expert verified
Equal matrices are matrices that have identical sizes (i.e., the same number of rows and columns), and all corresponding elements inside them are also the same.

Step by step solution

01

Definition

Equal matrices are two matrices that have the same dimensions and the same elements in their corresponding positions.
02

Conditions for Equality

For two matrices to be equal, they must satisfy two conditions: (i) They must have the same dimensions. That is, the number of rows and columns should be the same for both matrices. (ii) Corresponding elements in both matrices should be equal. That is, for an element in the nth row and mth column of the first matrix, the corresponding element in the nth row and mth column of the second matrix should be equal.

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Most popular questions from this chapter

Evaluate each determinant. $$ \left|\begin{array}{rrr}1 & 1 & 1 \\\2 & 2 & 2 \\\\-3 & 4 & -5\end{array}\right| $$

In Exercises \(17-26,\) 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 \(X\). $$ 2 X+5 A=B $$

In Exercises \(9-16,\) find: a. \(A+B\) b. \(A-B\) c. \(-4 A\) d. \(3 A+2 B\) .$$ A=\left[\begin{array}{lll} 6 & 2 & -3 \end{array}\right], \quad B=\left[\begin{array}{lll} 4 & -2 & 3 \end{array}\right] $$

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