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# Matrices Questions - All Grades

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Evaluate. $[[3,-9,5],[0,-1,4]] - [[4,-3,-11],[-3,0,7]]$
1. $[[-1,-12,-6],[-4,-1,-3]]$
2. $[[-1,6,-16],[3,1,-3]]$
3. $[[-1,-6,16],[3,-1,-3]]$
4. Cannot subtract because they are not square matrices.
Find the resulting matrix if the matrix $[[4,-2],[8,6]]$ is multiplied by $3/2$.
1. $[[6,-3],[12,9]]$
2. $[[12,-6],[24,18]]$
3. $[[6,-2],[12,6]]$
4. $[[6,-3],[8,6]]$
Add the following matrices. $[[4,-3],[-1,6]] + [[3,5],[2,-8]]$
1. $[[7,8],[3,14]]$
2. $[[7,2],[1,-2]]$
3. $[[9,0],[-9,8]]$
4. $[[7,-2],[-3,-2]]$
Subtract the matrices. $[[3,-9,2]] - [[5],[8],[-3]]$
1. $[[-2,-17,5]]$
2. $[[-2],[-17],[5]]$
3. $[[0,-5,0],[3,-17,2],[0,3,0]]$
4. Cannot subtract matrices of different dimensions.
Multiply the matrices, if possible. $[[3,4],[-2,5],[0,2]] * [[4,-1],[5,3]]$
1. $[[8,-13,-2],[27,5,6]]$
2. $[[12,-4],[-10,15],[0,2]]$
3. $[[32,9],[17,17],[10,6]]$
4. Not possible.
Evaluate. $[[5,4],[-3,8],[-2,1]] + [[1,0],[-5,5],[9,-2]]$
1. $[[6,4],[2,3],[7,-1]]$
2. $[[5,5],[ 2,3],[-4,10]]$
3. $[[6,4],[-8,13],[7,-1]]$
4. Not possible to add (they are not square matrices).
Evaluate. $[[4,8,-1,-1,3]] * [[2],[0],[-1],[3],[4]]$
1. $[18]$
2. $[[8],[0],[1],[-3],[12]]$
3. $[[8,0,1,-3,12]]$
4. These matrices cannot be multiplied together.
$y = 2/5 x + 3$
$6x-y=7$

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.
Solve the following matrix equation.
$[[3,-5],[-4,9]] [[x],[y]] = [[4],[4]]$
1. No Solution
2. $(8, 4)$
3. $(65, 28)$
4. $(16/7, -4/7)$
Which augmented matrix represents the system of equations $2x=8$ and $6=3y+x$?
1. $[[2,8,,0],[6,3,,1]]$
2. $[[8,2,,0],[6,3,,1]]$
3. $[[0,2,,8],[6,3,,1]]$
4. $[[2,0,,8],[1,3,,6]]$
If the matrix $[[2,9,8],[0,3,4],[1,11,3]]$ is multiplied by the scalar 5, what is the result?
1. $[[7,14,13],[5,8,9],[6,16,8]]$
2. $[[10,45,40],[0,15,20],[5,55,15]]$
3. $[[3,4,1],[11,3,2],[9,8,0]]$
4. $[[10,0,5],[45,15,55],[40,20,15]]$
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. $y=11, \ \ 2x+y=8$
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. $[[2,-7],[5,2]][[x],[y]] = [[11],[6]]$
Find the inverse of the following matrix, if it exists. $[[4,-3,8],[1,0,2],[-5,6,4]]$
1. There is no inverse of this matrix.
2. $[[-2/7, 10/7, -1/7],[-1/3, 4/3, 0],[1/7, -3/14, 1/14]]$
3. $[[2/7, -10/7, 1/7],[1/3, -4/3, 0],[-1/7, 3/4, -1/4]]$
4. $[[-2/7, -10/7, -1/7],[1/3, 4/3, 0],[1/7, 3/4, 1/4]]$
For $M = [[4,-5],[-3,6]]$, find $M^{-1}$, if it exists.
1. Matrix M does not have an inverse.
2. $[[2/13, 5/39],[1/13, 4/39]]$
3. $[[2/3, 5/9],[1/3, 4/9]]$
4. $[[4/9, -5/9],[-1/3, 2/3]]$
If A is a given square matrix, and it is known that there exists a matrix B such that $AB=1$, which of the following would be the most efficient ways to find the matrix B?
1. Find the inverse of A. This is the matrix B.
2. Find the transpose of A. This is the matrix B.
3. Create a matrix B whose elements are variables. Then, perform matrix multiplication with the matrix A, setting each resulting entry equal to one. Solve this system of equations, which will give the elements of matrix B.
4. Multiply both sides of the equation, on the left, by slight variations of the matrix A. When one of these matrices, multiplied by A, becomes the identity matrix, this is the matrix B.