## SAT SUBJECT TEST MATH LEVEL 2

## PART 2

## REVIEW OF MAJOR TOPICS

## CHAPTER 3

## Numbers and Operations

3.3 Matrices

### SOLVING SYSTEMS OF EQUATIONS

An important application of matrices is writing and solving systems of equations in matrix form.

**EXAMPLE**

**Solve the system**

This system can be written as *AV* = *B* , where *A* = is the matrix of the

coefficients, is the matrix of the variables, and is the column matrix representing the right side of the system. Multiplying both sides of this equation on the left by *A*^{–1} yields *A*^{–1}*AV* = *A*^{–1}*B* , which reduces to *V* = *A*^{–1}*B*. If given a system of equations, enter the matrix of coefficients into a matrix (*A* ), the column matrix of the right side into a second matrix (*B* ), and find the product *A*^{–1}*B* to display the solution.

**EXERCISES**

1. Find the matrix equation that represents the system

(A)

(B)

(C)

(C)

(E) This system cannot be represented as a matrix equation.

2. Find .

(A) (–2 0.5)

(B)

(C) (–1 3/4)

(D)

(E) (–5 –4/5)