Matrices Quiz

Grade 11 · Math · Quiz

10 questions on matrix dimensions, operations, determinants, and inverses.

Questions

1. A matrix has 4 rows and 2 columns. What are its dimensions?

   1. 2x4
   2. 4x2
   3. 8x1
   4. 4x4
   Show answer

   Answer: 4x2

   Dimensions are rows x columns: 4 rows and 2 columns = 4x2.

2. Can you multiply a 3x2 matrix by a 3x4 matrix (in that order)?

   1. Yes, result is 3x4
   2. No, inner dimensions do not match
   3. Yes, result is 2x4
   4. Yes, result is 3x3
   Show answer

   Answer: No, inner dimensions do not match

   cols(A)=2 must equal rows(B)=3. 2 != 3, so multiplication is not defined.

3. What is det([[6, 0],[1, 3]])?

   1. 18
   2. 6
   3. 3
   4. 21
   Show answer

   Answer: 18

   det = (6)(3) - (0)(1) = 18 - 0 = 18.

4. Scalar multiply: 3 * [[1, -2],[0, 4]].

   1. [[3,-6],[0,12]]
   2. [[3,2],[0,4]]
   3. [[1,-6],[0,12]]
   4. [[4,1],[3,7]]
   Show answer

   Answer: [[3,-6],[0,12]]

   Multiply each element by 3: [3, -6; 0, 12].

5. The identity matrix I_2 is:

   1. [[1,0],[0,1]]
   2. [[0,1],[1,0]]
   3. [[1,1],[1,1]]
   4. [[2,0],[0,2]]
   Show answer

   Answer: [[1,0],[0,1]]

   The 2x2 identity has 1s on the diagonal and 0s elsewhere.

6. If det(A) = 0, what can you conclude?

   1. A is the identity
   2. A has an inverse
   3. A is not invertible (singular)
   4. A is a scalar
   Show answer

   Answer: A is not invertible (singular)

   A matrix is invertible if and only if its determinant is nonzero.

7. Multiply: [[2,0],[0,3]] * [[1,4],[5,2]].

   1. [[2,8],[15,6]]
   2. [[2,4],[5,6]]
   3. [[2,8],[0,6]]
   4. [[7,8],[5,5]]
   Show answer

   Answer: [[2,8],[15,6]]

   Row1*Col1: 2(1)+0(5)=2; Row1*Col2: 2(4)+0(2)=8; Row2*Col1: 0(1)+3(5)=15; Row2*Col2: 0(4)+3(2)=6.

8. To solve AX = B for X using matrix algebra, you compute:

   1. X = BA^(-1)
   2. X = A^(-1)B
   3. X = AB
   4. X = B/A
   Show answer

   Answer: X = A^(-1)B

   Multiply both sides on the left by A^(-1): X = A^(-1)B.

9. What is the determinant of the 2x2 identity matrix?

   1. 0
   2. 2
   3. 1
   4. -1
   Show answer

   Answer: 1

   det([[1,0],[0,1]]) = (1)(1) - (0)(0) = 1.

10. Subtract: [[7,3],[1,5]] - [[2,1],[4,2]].

    1. [[5,2],[-3,3]]
    2. [[5,4],[5,7]]
    3. [[9,4],[5,7]]
    4. [[5,2],[3,3]]
    Show answer

    Answer: [[5,2],[-3,3]]

    [7-2, 3-1; 1-4, 5-2] = [5,2;-3,3].

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