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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.
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).
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.
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. $[[10,0,5],[45,15,55],[40,20,15]]$
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. $[[-6,11],[2,-7],[4,14]]$
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. $[[9,1,6],[3,0,7],[4,2,1]]$
For given matrices A and B, let $A \ B = M$, where M is a also a matrix. Which of the following correctly describes the dimensions of matrix M?