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CHAPTER 16 PRACTICE TEST

As a study aid, we have included complete solutions for each Practice Test problem at the end of this book.

For matrices A and B, find $A - 2 B .$ $A - 2 B .$

$A = [\begin{array}{r} 3 & - 1 & 4 \\ 2 & 0 & - 2 \end{array}] B = [\begin{array}{r} 1 & 4 & 5 \\ - 1 & - 2 & 3 \end{array}]$ $A = [\begin{array}{r} 3 & - 1 & 4 \\ 2 & 0 & - 2 \end{array}] B = [\begin{array}{r} 1 & 4 & 5 \\ - 1 & - 2 & 3 \end{array}]$
Evaluate the literal symbols.

$[\begin{array}{c} 2 x & x - y & z \\ x + z & 2 y & y + z \end{array}] = [\begin{array}{c} 6 & - 2 & 4 \\ a & b & c \end{array}]$ $[\begin{array}{c} 2 x & x - y & z \\ x + z & 2 y & y + z \end{array}] = [\begin{array}{c} 6 & - 2 & 4 \\ a & b & c \end{array}]$
For matrices C and D, find CD and DC, if possible.

$C = [\begin{array}{r} 1 & 0 & 4 \\ 2 & - 2 & 1 \\ - 1 & 3 & 2 \end{array}] D = [\begin{array}{r} 2 & - 2 \\ 4 & - 5 \\ 6 & 1 \end{array}]$ $C = [\begin{array}{r} 1 & 0 & 4 \\ 2 & - 2 & 1 \\ - 1 & 3 & 2 \end{array}] D = [\begin{array}{r} 2 & - 2 \\ 4 & - 5 \\ 6 & 1 \end{array}]$
Determine whether or not $B = A^{- 1} .$ $B = A^{- 1} .$

$A = [\begin{array}{l} 2 & - 5 \\ 1 & - 2 \end{array}] B = [\begin{array}{l} - 2 & 5 \\ - 1 & 2 \end{array}]$ $A = [\begin{array}{l} 2 & - 5 \\ 1 & - 2 \end{array}] B = [\begin{array}{l} - 2 & 5 \\ - 1 & 2 \end{array}]$
For matrix C of Problem 3, find $C^{- 1} .$ $C^{- 1} .$
Solve by using the inverse of the coefficient matrix.

$\begin{array}{rcl} 2 x - 3 y & = & 11 \\ x + 2 y & = & 2 \end{array}$ $\begin{array}{rcl} 2 x - 3 y & = & 11 \\ x + 2 y & = & 2 \end{array}$
Solve the system of equations in Problem 6 by Gaussian elimination.
Evaluate the following determinant by expansion by minors.

$| \begin{array}{r} 2 & - 4 & - 3 \\ - 3 & 6 & 2 \\ 5 & - 1 & 5 \end{array} |$ $| \begin{array}{r} 2 & - 4 & - 3 \\ - 3 & 6 & 2 \\ 5 & - 1 & 5 \end{array} |$
Solve the following system of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the result and check. Write down the display shown in the window with the solutions.

$\begin{array}{rcrcl} 7 x - 2 y & + & z & = & 6 \\ 2 x + 3 y & - & 4 z & = & 6 \\ 4 x - 5 y & + & 2 z & = & 10 \end{array}$ $\begin{array}{rcrcl} 7 x - 2 y & + & z & = & 6 \\ 2 x + 3 y & - & 4 z & = & 6 \\ 4 x - 5 y & + & 2 z & = & 10 \end{array}$
Fifty shares of stock A and 30 shares of stock B cost $2600. Thirty shares of stock A and 40 shares of stock B cost $2000. What is the price per share of each stock? Solve by setting up the appropriate equations and then using the inverse of the coefficient matrix.

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Table of Contents for CHAPTER 16 PRACTICE TEST

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Table of Contents for
CHAPTER 16 PRACTICE TEST