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# Eleventh Grade (Grade 11) Matrices Questions

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Grade 11 Matrices CCSS: HSA-REI.C.5
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. $y=11, \ \ 2x+y=8$
Grade 11 Matrices
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.
Grade 11 Matrices CCSS: HSA-REI.C.8
$y = 2/5 x + 3$
$6x-y=7$

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.
Grade 11 Matrices CCSS: HSN-VM.C.8
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
Grade 11 Matrices
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.
Grade 11 Matrices CCSS: HSN-VM.C.7
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. $"Does not exist (because of 0 in matrix)"$
Grade 11 Matrices CCSS: HSN-VM.C.8
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
Grade 11 Matrices CCSS: HSN-VM.C.8
Evaluate. $[[1,2],[3,4]]+[[1,2],[3,4]]$
1. $[[2,4],[6,8]]$
2. $[[2,8],[6,4]]$
3. $[[8,2],[6,4]]$
Grade 11 Matrices
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. $3xx4$
Grade 11 Matrices CCSS: HSN-VM.C.8
Evaluate, if possible.
$[[3,4,8],[1,3,1]] + [[6,1],[9,2],[3,4]]$
1. $[[9,2],[13,5],[11,5]]$
2. $"Not possible"$
3. $[[9,5],[10,5]]$
4. $[[7,4],[12,6],[4,12]]$
Grade 11 Matrices CCSS: HSN-VM.C.8
Evaluate, if possible. $[[-5,7],[6,8]] - [[4,0,-2],[9,0,1]]$
1. $[[-9,7],[-3,8]]$
2. $[[13,-7],[3,-8]]$
3. $[[-9,7,4],[-3,8,-13]]$
4. Impossible
Grade 11 Matrices CCSS: HSA-REI.C.9
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. $(-1,-1)$
Grade 11 Matrices
A square matrix A is NOT invertible (does not have an inverse) if which of the following is true?
1. Matrix A is the identity matrix
2. $A_{1,1} < 0$
3. Matrix A has any elements equal to zero
4. $det(A) = 0$
Grade 11 Matrices CCSS: HSN-VM.C.8
Find the product, if possible. $[[2,0],[-3,5],[1,4]]*[[3],[-2]]$
1. $[[6,-19,-5]]$
2. $[[6],[-19],[-5]]$
3. $[[5,-5],[0,3]]$
4. Impossible
Grade 11 Matrices
Which of the following can you not do when solving a system of equations using matrices?
1. Add two rows.
2. Switch two rows.
3. Add a constant to a row.
4. Multiply a row by a constant.
Grade 11 Matrices
Find the inverse of the matrix, if it exists.

$[[-4,-2],[7,8]]$
1. $"Does Not Exist"$
2. $[[4/9,1/9],[-7/18,-2/9]]$
3. $[[2/9,1/9],[-7/18,-4/19]]$
4. $[[-4/9,-1/9],[7/18,2/9]]$
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