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Twelfth Grade (Grade 12) Matrices Questions

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Grade 12 Matrices CCSS: HSN-VM.C.8
Evaluate. [math][[3,-9,5],[0,-1,4]] - [[4,-3,-11],[-3,0,7]] [/math]
  1. [math] [[-1,-12,-6],[-4,-1,-3]] [/math]
  2. [math] [[-1,6,-16],[3,1,-3]] [/math]
  3. [math] [[-1,-6,16],[3,-1,-3]][/math]
  4. Cannot subtract because they are not square matrices.
Grade 12 Matrices CCSS: HSN-VM.C.7
Find the resulting matrix if the matrix [math][[4,-2],[8,6]][/math] is multiplied by [math]3/2[/math].
  1. [math] [[6,-3],[12,9]] [/math]
  2. [math] [[12,-6],[24,18]][/math]
  3. [math] [[6,-2],[12,6]] [/math]
  4. [math] [[6,-3],[8,6]] [/math]
Grade 12 Matrices CCSS: HSN-VM.C.8
Add the following matrices. [math] [[4,-3],[-1,6]] + [[3,5],[2,-8]][/math]
  1. [math] [[7,8],[3,14]][/math]
  2. [math] [[7,2],[1,-2]] [/math]
  3. [math] [[9,0],[-9,8]] [/math]
  4. [math] [[7,-2],[-3,-2]] [/math]
Grade 12 Matrices CCSS: HSN-VM.C.8
Subtract the matrices. [math][[3,-9,2]] - [[5],[8],[-3]][/math]
  1. [math] [[-2,-17,5]][/math]
  2. [math][[-2],[-17],[5]][/math]
  3. [math][[0,-5,0],[3,-17,2],[0,3,0]][/math]
  4. Cannot subtract matrices of different dimensions.
Grade 12 Matrices CCSS: HSN-VM.C.8
Evaluate. [math] [[5,4],[-3,8],[-2,1]] + [[1,0],[-5,5],[9,-2]] [/math]
  1. [math] [[6,4],[2,3],[7,-1]][/math]
  2. [math] [[5,5],[ 2,3],[-4,10]][/math]
  3. [math] [[6,4],[-8,13],[7,-1]][/math]
  4. Not possible to add (they are not square matrices).
Grade 12 Matrices CCSS: HSN-VM.C.8
Multiply the matrices, if possible. [math] [[3,4],[-2,5],[0,2]] * [[4,-1],[5,3]] [/math]
  1. [math] [[8,-13,-2],[27,5,6]][/math]
  2. [math] [[12,-4],[-10,15],[0,2]] [/math]
  3. [math] [[32,9],[17,17],[10,6]][/math]
  4. Not possible.
Grade 12 Matrices CCSS: HSN-VM.C.6
Which augmented matrix represents the system of equations [math]2x=8[/math] and [math]6=3y+x[/math]?
  1. [math][[2,8,,0],[6,3,,1]][/math]
  2. [math][[8,2,,0],[6,3,,1]][/math]
  3. [math][[0,2,,8],[6,3,,1]][/math]
  4. [math][[2,0,,8],[1,3,,6]][/math]
Grade 12 Matrices CCSS: HSN-VM.C.8
Evaluate. [math] [[4,8,-1,-1,3]] * [[2],[0],[-1],[3],[4]] [/math]
  1. [math] [18] [/math]
  2. [math] [[8],[0],[1],[-3],[12]] [/math]
  3. [math] [[8,0,1,-3,12]][/math]
  4. These matrices cannot be multiplied together.
Grade 12 Matrices CCSS: HSN-VM.C.7
If the matrix [math][[2,9,8],[0,3,4],[1,11,3]][/math] is multiplied by the scalar 5, what is the result?
  1. [math][[7,14,13],[5,8,9],[6,16,8]][/math]
  2. [math][[10,45,40],[0,15,20],[5,55,15]][/math]
  3. [math][[3,4,1],[11,3,2],[9,8,0]][/math]
  4. [math][[10,0,5],[45,15,55],[40,20,15]][/math]
Grade 12 Matrices CCSS: HSN-VM.C.10
Grade 12 Matrices CCSS: HSN-VM.C.8
Find the difference. [math] [[2,0],[-4,1],[8,12],[0,-3],[1,1]] - [[-3,5],[6,10],[3,12],[-4,4],[8,7]] [/math]
  1. [math] [[5,5],[-2,-9],[-5,-24],[-4,1],[-7,-6]] [/math]
  2. [math] [[5,-5],[-10,-9],[5,0],[4,-7],[-7,-6]][/math]
  3. [math] [[-1,5],[2,11],[11,24],[-4,1],[9,8]] [/math]
  4. [math] [[-5,-5],[-2,9],[5,24],[-4,-7],[7,6]][/math]
Grade 12 Matrices CCSS: HSN-VM.C.8
Add. [math] [[4,9,-6],[-3,0,8],[2,2,5]] + [[-10, 2,6],[5,-7,-8],[2,12,-5]] [/math]
  1. [math] [[-6,11,0],[2,-7,0],[4,14,0]] [/math]
  2. [math] [[14,11,12],[8,-7,16],[4,14,10]] [/math]
  3. [math] [[-14, 7,-12],[-8,7,16],[0,-10,10]][/math]
  4. [math] [[-6,11],[2,-7],[4,14]] [/math]
Grade 12 Matrices CCSS: HSN-VM.C.10
If A is a given square matrix, and it is known that there exists a matrix B such that [math]AB=1[/math], 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.
Grade 12 Matrices CCSS: HSN-VM.C.7
If the matrix [math][[27,9,12],[3,0,6],[18,21,3]][/math] is multiplied by the scalar [math]1/3[/math], what is the result?
  1. [math][[9,3,4],[1,0,2],[6,7,1]][/math]
  2. [math][[30,12,14],[6,3,9],[21,24,6]][/math]
  3. [math][[27,9,12],[3,0,6],[18,21,3]][/math]
  4. [math][[9,1,6],[3,0,7],[4,2,1]][/math]
Grade 12 Matrices CCSS: HSN-VM.C.9
Grade 12 Matrices CCSS: HSN-VM.C.8
For given matrices A and B, let [math]A \ B = M[/math], where M is a also a matrix. Which of the following correctly describes the dimensions of matrix M?
  1. Number of rows of A, number of columns of B.
  2. Number of rows of B, number of columns of A.
  3. Number of rows of A, number of columns of A.
  4. Number of rows of B, number of columns of B.
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