## SAT SUBJECT TEST MATH LEVEL 2

## PART 2

## REVIEW OF MAJOR TOPICS

## CHAPTER 3

## Numbers and Operations

3.3 Matrices

### Answers and Explanations

Addition, Subtraction, and Scalar Multiplication

1. **(C)** First find the sum of the matrices to the left of the equals sign: . Since the first row of the matrix to the right of the equals sign is (3 2), *K* must be 4. Since (*J M* ) is the bottom row, *J* = –2 and *M* = 4. Therefore, *K* + *J* + *M* = 6.

2. **(E)** In order for these matrices to be equal, .

Therefore, *x* = 2*x*^{2} and *y* = 6*y* – 10. Solving the first equation yields *x* = 0, and *y* = 2.

3. **(B)** To solve for *X* , first subtract from both sides of the equation.

Then .

Matrix Multiplication

1. **(B)** By definition, *AB* = = [−37 21]

2. **(C)** By definition, the first row, second column of the product is (*x* )(–*x* ) + (1)(1) = –*x*^{2} + 1.

3. **(B)** *X* must have as many rows as *A* has columns, which is 3. *X* must have as many columns as *B* does, which is 2.

4. **(B)** Matrix multiplication is row by column. Since the answer must be a 3 by 1 matrix, the only possible answer choice is B.

Determinants and Inverses of Square Matrices

1. **(B)** By definition, the determinant of is (*p* )(1) – (3)(–2) = *p* + 6.

2. **(B)** Enter the 3 by 3 matrix on the left side of the equation into your graphing calculator and evaluate its determinant (zero). The determinant on the right side of the equation is *x*^{2} – 20. Therefore *x* = ± ±4.47.

3. * **(C)** To find *X* , multiply both sides of the equation by on the right. Enter both matrices in your calculator, key the product on your graphing calculator, and key MATH/ENTER/ENTER to convert the decimal answer to a fraction.

Solving Systems of Equations

1. **(B)** First, write the system in standard form: . The matrix form of this equation is .

2. * **(D)** This is the matrix form *AX* = *B* of a system of equations. Multiply both sides of the equation by *A*^{–1} on the left to get the solution *X* = = *A*^{–1}*B*. Enter the 2 by 2 matrix, *A* , and the 2 by 1 matrix, *B* , into your graphing calculator. Return to the home screen and enter *A*^{–1}*B* = .