9.5+OFSA

OFSA for Matrix Theory
This page contains peer generated questions that help you assess your understanding. Remember that questions may not represent the rigor of the questions you may be expected to complete on formal assessments. This page is simply an OFSA - opportunity for self assessment.


 * Question 1**

math \left[ {\begin{array}{*{20}{c}} {2x + y}&8 \\ 9&y \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} {3x}&{x - y} \\ 4&x \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {17}&9 \\ {13}&5 \end{array}} \right] math

Solve for x and y.

A) math \begin{gathered} x = 3 \hfill \\ y = 2 \hfill \\ \end{gathered} math

B) math \begin{gathered} x =\frac{6} \hfill \\ y =\frac{3} \hfill \\ \end{gathered} math

C) math \begin{gathered} x = 2 \hfill \\ y = 3 \hfill \\ \end{gathered} math

D) math \begin{gathered} x = 1 \hfill \\ y = 12 \hfill \\ \end{gathered} math

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 * Question 2**

math \left[ {\begin{array}{*{20}{c}} {2a}&b \\ e&d \end{array}} \right] - \left[ {\begin{array}{*{20}{c}} c&c \\ d&{ - 2e} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} b&d \\ 5&c \end{array}} \right] math

Solve for a in terms of e

A) math a=7e-5 math

B) math a=7e-15 math

C) math a=(7e-5)/2 math

D) math a=(7e-15)/2 math

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 * Question 3**

There are 3 vendors of tuna in Gillsville NJ. Each sells blue tuna, yellow tuna, and red tuna. Last week, Vendor 1 sold 30 blue tuna, 15 yellow tuna, and 22 red tuna. Vendor 2 sold 27 blue tuna, 10 yellow tuna, and 14 red tuna. Vendor 3 sold 18 blue tuna, 8 yellow tuna, and 12 red tuna. Blue tuna costs $10, yellow costs $8, and red costs $6 per fish. How much income did Vendor 1 make last week? (Use matrices)

A) $750

B) $552

C) $434

D) Impossible to solve with matrices

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math \[\begin{bmatrix} 4 &-3 \\ 1 &2 \\ 7& 7\\ -3&3 \\ 6& 4 \end{bmatrix}X \begin{bmatrix} 4\\ -4 \end{bmatrix}=A\] math Solve for A a) math \[\begin{bmatrix} 8\\ -24\\ 0\\ -4\\ 28 \end{bmatrix}\] math b) math \[\begin{bmatrix} 4&-4 \\ 12&-12 \\ 56&-56 \\ 0&0 \\ 40&40 \end{bmatrix}\] math c) math \[\begin{bmatrix} 28\\ -4\\ 0\\ -24\\ 8 \end{bmatrix}\] math d) does not exist
 * Question 4**

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solve for the determinant and inverse of math \[\begin{bmatrix} 7&-1 \\ 3&-1 \end{bmatrix}\] math a) d=-1/4 math \[\begin{bmatrix} 1/4 & -1/4\\ 3/4& -7/4 \end{bmatrix}\] math b) d=1 math \[\begin{bmatrix} -1& 1\\ -3& 7 \end{bmatrix}\] math c) does not exist d) d=1/4 math \[\[\begin{bmatrix} -1/4 & 1/4\\ -3/4& 7/4 \end{bmatrix}\]\] math Click here for solution.
 * Question 5**


 * Question 6**

Decompose the following fraction using Partial Fraction Decomposition: math \frac{-x-2}{x^2+10x+24} math math a)\[\frac{-x}{x+6}-\frac{2}{x+4}\] math math b)\[\frac{-x}{x+4}-\frac{2}{x+6}\] math math c)\[\frac{-2}{x+6}+\frac{1}{x+4}\] math d) No Solution - Fraction cannot be decomposed

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solve for the following matrix using REF math \begin{bmatrix} 1& -2& 1& 1\\ 0& 1& 2& 5\\ 1& 1& 3& 8 \end{bmatrix} math a) no solution b) (-6.5, -2, 3.5) c) (8-3p,5-2p,p) where z is replaced by parameter p where p is all real numbers d)(4,-3,-9) Click here for solution.
 * Question 7**


 * Question 8**

Given the following matrix:

math \[\begin{bmatrix}

6 &n+5 \\

n-3 &-2

\end{bmatrix}\] math

Solve for n so that the inverse of the matrix is defined.

a) n must equal -3 and 1 b) n must not equal -3 and 1 c) The inverse is defined for all values of n d) The inverse is undefined for all values of n

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 * Question 9**

Which one of the following choices is an identity matrix?

math a) \[\begin{bmatrix}

0 &1 \\

1 &0

\end{bmatrix}\] math math b) \[\begin{bmatrix}

1 &0 &0 \\

0 &1 &0 \\

0 &0 &1

\end{bmatrix}\] math math c) \[\begin{bmatrix}

0 &0 \\

0& 0

\end{bmatrix}\] math math d) \[\begin{bmatrix}

1 &0 \\

0& 1\\

0&0

\end{bmatrix}\] math

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math \begin{bmatrix} 6 & 3\\ 12 & 6 \end{bmatrix} math a) math \begin{bmatrix} 6 & -3\\ -12 & 6 \end{bmatrix} math b) math \begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix} math c) math \begin{bmatrix} 36 & 144\\ 9& 36 \end{bmatrix} math d) does not exist Click here for solution.
 * Question 10**
 * solve for inverse by hand**

Decompose the expression math \[\frac{2x^2+x-12}{x^3+5x^2+6x}\]
 * Question 11**

a) \[\frac{-2}{x}+\frac{1}{x+3}+\frac{3}{x+2}\]

b) \[\frac{1}{x}+\frac{3}{x+3}+\frac{-2}{x+2}\]

c) \[\frac{2}{x}+\frac{6}{x+3}+\frac{-4}{x+2}\] math d) no solution e) none of the above

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 * Question 12**

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 * Question 13**

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 * Question 14**

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 * Question 15**

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 * Question 16**

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 * Question 17**

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 * Question 18**

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 * Question 19**

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 * Question 20**

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 * Question 22**

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 * Question 23**

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 * Question 24**