﻿ ADDITION, SUBTRACTION, AND SCALAR MULTIPLICATION - Matrices - Numbers and Operations - REVIEW OF MAJOR TOPICS - SAT SUBJECT TEST MATH LEVEL 2 ﻿

## PART 2 ## REVIEW OF MAJOR TOPICS ## Numbers and Operations

### 3.3 Matrices ### ADDITION, SUBTRACTION, AND SCALAR MULTIPLICATION

A matrix is a rectangular array of numbers. The size of a matrix is r by c , where r is the number of rows and c is the number of columns. The numbers in a matrix are called entries, and the entry in the i th row and j th column is named xij. Two matrices are equal if they are the same size and their corresponding entries are equal.

EXAMPLES

1. Evaluate x and y if .

These two matrices are equal if y – 3 = 5 and x = 2x + 2. Therefore, y = 8 and x = –2.

If r = 1, the matrix is called a row matrix. If c = 1, the matrix is called a column matrix. If r = c , the matrix is called a square matrix. The numbers from the upper left corner to the bottom right corner of a square matrix form the main diagonal.

Scalar multiplication takes place when each number in a matrix is multiplied by a constant. If two matrices are the same size, they can be added or subtracted by adding or subtracting corresponding entries.

2. Simplify:  3. Solve the matrix equation:   EXERCISES

1. . Find the value of K + J + M.

(A)  2

(B)  4

(C)  6

(D)  7

(E)  8

2. Evaluate x and if .

(A)  x = 0; y = 2

(B)  x = 1; y = 2

(C)  x = −1, 1; (D) (E)  x = 0, y = 2

3. Solve for x .

(A) (B) (C) (D) (E) ﻿

﻿