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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. $[[6,-3],[8,6]]$
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.
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. $[[7,-2],[-3,-2]]$
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.
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.
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).
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. $[[2,0,,8],[1,3,,6]]$
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.
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. $[[10,0,5],[45,15,55],[40,20,15]]$
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.
If the matrix $[[27,9,12],[3,0,6],[18,21,3]]$ is multiplied by the scalar $1/3$, what is the result?
1. $[[9,3,4],[1,0,2],[6,7,1]]$
2. $[[30,12,14],[6,3,9],[21,24,6]]$
3. $[[27,9,12],[3,0,6],[18,21,3]]$
4. $[[9,1,6],[3,0,7],[4,2,1]]$
James needs to show that for matrix $A = [[5,-2,1],[3,3,2],[-6,3,-1]]$, there is no matrix $B, B!=I$, such that $AB = I$, where $I$ is the 3-by-3 identity matrix. How can he do this?
1. Try at least 3 matrices, and if none of them multiplied by $A$ equal the identity matrix, then it is not possible.
2. Find the inverse of $A$, and then show that since this matrix is unique, there cannot exist another matrix $B$ such that $AB = I$.
3. Subtract by the additive inverse on both sides, and then factor the left hand side of the equation. This implies that if $B=I$ the equation equals the zero matrix, which it can't.
4. Show that the determinant of $A$ is zero, which means that it does not have a multiplicative inverse.
If Matrix A = $[(-3,1),(-2,4),(5,-1)]$ and Matrix B = $[(4,-3),(0,-2),(-2,4)]$, then what is 3A - 2B?
1. $[(-1,-3),(-6,8),(11,5)]$
2. $[(-1,9),(-6,8),(11,5)]$
3. $[(-1,9),(-6,8),(11,-11)]$
4. $[(-17,9),(-6,16),(19,-11)]$
The vertex matrix for rectangle ABCD is $V = [[1,1,4,4],[1,3,3,1]]$. Which of the following is the correct transformed vertex matrix, if the transformation matrix $A = [[0,1],[-1,0]]$ is applied?
1. $[[1,-1],[3,-1],[3,-4],[1,-4]]$
2. $[[-1,-3,-3,-1],[1,1,4,4]]$
3. $[[1,3,3,1],[-1,-1,-4,-4]]$
4. $[[-1,-3,-3,-1],[-1,-1,-4,-4]]$
For the transformation matrix $A = [[1,0],[0,-1]]$, how is the vector $vec{v} = <<3, 4>>$ affected if it is multiplied with $A ?$
1. It has been rotated 90° clockwise.
2. It has reversed direction.
3. It has been reflected over a horizontal line.
4. The resulting transformation is a combination of reflections and rotations.
Find the difference. $[[2,0],[-4,1],[8,12],[0,-3],[1,1]] - [[-3,5],[6,10],[3,12],[-4,4],[8,7]]$
1. $[[5,5],[-2,-9],[-5,-24],[-4,1],[-7,-6]]$
2. $[[5,-5],[-10,-9],[5,0],[4,-7],[-7,-6]]$
3. $[[-1,5],[2,11],[11,24],[-4,1],[9,8]]$
4. $[[-5,-5],[-2,9],[5,24],[-4,-7],[7,6]]$
Add. $[[4,9,-6],[-3,0,8],[2,2,5]] + [[-10, 2,6],[5,-7,-8],[2,12,-5]]$
1. $[[-6,11,0],[2,-7,0],[4,14,0]]$
2. $[[14,11,12],[8,-7,16],[4,14,10]]$
3. $[[-14, 7,-12],[-8,7,16],[0,-10,10]]$
4. $[[-6,11],[2,-7],[4,14]]$