## SAT SUBJECT TEST MATH LEVEL 2

## PART 2

## REVIEW OF MAJOR TOPICS

## CHAPTER 3

## 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 *x _{ij}*. 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* = 2*x* + 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 *y *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)