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 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)