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$y = 2/5 x + 3$
$6x-y=7$

Jake is going to solve the system of equations using a matrix equation. He sets up his matrix equation as follows.
$[[5, -2],[6,-1]] [[x],[y]] = [[3],[7]]$
Is this a correct? If not, choose the correct reason why not.
1. It is correct.
2. There must be a fraction in the matrix equation since there is one in the system of equations.
3. The coefficients don't match up to the correct variables in the matrix equation.
4. Systems of linear equations with equations not in standard form can never be put into a matrix equation.
Which of the following is an equivalent system of equations to the one given?

$3x+5y=5$
$2x+y=8$
1. $-7x = -35, \ \ 2x+y=8$
2. $3x+5y=5, \ \ -13x = -17$
3. $3x+5y=5, \ \ 2x=8$
4. $y=11, \ \ 2x+y=8$
Solve the following matrix equation.
$[[3,-5],[-4,9]] [[x],[y]] = [[4],[4]]$
1. No Solution
2. $(8, 4)$
3. $(65, 28)$
4. $(16/7, -4/7)$
What is the rule for matrix multiplication?
1. The number of columns of the first matrix must equal the number of rows of the second matrix.
2. The matrices must have the same dimensions.
3. The matrices must have the same number of rows, but not columns.
4. There is no rule. Matrix multiplication is always possible.
What is the rule for matrix addition and subtraction?
1. The number of columns of the first matrix must equal the number of rows of the second matrix.
2. The matrices must have the same dimensions.
3. The matrices must have the same number of rows, but not columns.
4. There is no rule. Matrix addition and subtraction is always possible.
Evaluate. $[(2, -3) , (-4, 2)]$ + $[ (-1, -5), ( 3, -2) ]$
1. $[(-1, -8), (-1, 0)]$
2. $[(1, -8), (-1,0)]$
3. $[(1, -8), (-7, 0)]$
4. None of the above
Which matrix equation represents the following system of equations?
$2x-7y=11$
$2y+5x=6$
1. $[[2,-7],[2,5]] [[x],[y]] = [[11],[6]]$
2. $[[2,-7],[2,5]] [[11],[6]] = [[x],[y]]$
3. $[[2,7],[5,2]] [[x],[y]] = [[11],[6]]$
4. $[[2,-7],[5,2]][[x],[y]] = [[11],[6]]$
State the dimensions of matrix $F$ if $F=[[0,1,0],[2,-4,2],[4,-8,4],[8,-16,8]]$ .
1. $16xx8$
2. $2xx2xx3$
3. $4xx3$
4. $3xx4$
Evaluate. $[(2,-3), (-4,2)] - [(-1,-5), (-3,2)]$
1. $[(3,2),(-7,4)]$
2. $[(-3,2),(-7,4)]$
3. $[(3,2),(-1,0)]$
4. None of the above
Solve the matrix equation.
$[[3,4],[1,4/3]] [[x],[y]] = [[9],[4/3]]$
1. The inverse does not exist (the matrix is singular).
2. $(-640/27, 160/9)$
3. $(160/3,-40)$
4. $(416/3, 104)$
Solve the matrix equation.
$[[-1/3, 2],[5,-7]] [[x],[y]] = [[1],[8]]$
1. $(-27/23, -7/23)$
2. $(69/37, 23/37)$
3. $(1,8)$
4. $(3,1)$
When representing a system of linear equations in two variables as a matrix equation, one can use the general form $A [[x],[y]] = vec[b]$. For a given system of linear equations, is it possible for the 2-by-2 matrix $A$ to have different entries? Why or why not?
1. Yes. Either equation in the system of equations can be multiplied by a constant. This will also affect $vec(b)$.
2. No. A different matrix $A$ would result in a different answer regardless of anything else.
3. It depends on whether the system of equations is dependent or independent.
4. No. Only a system of equations that is inconsistent, and therefore has no answer anyways, can have different $A$ matrices.
Which matrix equation correctly represents the following linear system of equations?
$y=1/2 x + 3/4$
$5x-3y=3$
1. $[[1, 1/2],[5,-3]] [[x],[y]] = [[3/4],[3]]$
2. $[[-1/2,1],[5,-3]] [[x],[y]] = [[3/4],[3]]$
3. $[[4,2],[5,-3]] [[x],[y]] = [[3/4],[3]]$
4. $[[4,2],[-3,5]] [[x],[y]] = [[3],[3]]$
Evaluate. $[[1,2],[3,4]]+[[1,2],[3,4]]$
1. $[[2,4],[6,8]]$
2. $[[2,8],[6,4]]$
3. $[[8,2],[6,4]]$
For $A = [[16, 8, 32], [4, 0, 12], [8, 24, 20]]$, find $1/4 A$.
1. $[[4, 2, 8],[4, 0, 12], [8, 24, 20]]$
2. $[[ 4, 8, 32],[1, 0, 12],[2,24,20]]$
3. $[[4,2,8],[1,0,3],[2,6,5]]$
4. $"Does not exist (because of 0 in matrix)"$
Which matrix equation correctly represents the following system of equations?
$y=3/4 x -5/4$
$2y+x=5$
1. $[[-3 ,4],[1, 2]] [[x],[y]] = [[-5],[5]]$
2. $[[1,3/4],[2,1]] [[x],[y]] = [[-5/4],[5]]$
3. $[ [3/4, 1],[1,2]] [[x],[y]] = [[-5/4],[5]]$
4. $[[4,3],[2,1]] [[x],[y]] = [[-5],[4]]$
Find the solution of the following matrix equation $[[1,5],[1,6]][[x],[y]]=[[-4],[-5]]$.
1. $(1,-1)$
2. $(1,1)$
3. $(0,1)$
4. $(-1,-1)$