Matrices: size, entries, add, subtract and scalar multiples

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Row 1: -3, 9; row 2: 8, 5. Matrix B: row 1: -5, -5; row 2: -9, 6. Milo subtracts matrix B from matrix A. What is the entry in row 1, column 2 of A − B?

   14

2. Read this first

   Matrix A

   Row 1: -4, 7, 2; row 2: -6, 4, 4; row 3: -9, 7, 4. Matrix B: row 1: 1, -8, -5; row 2: 1, 1, -6; row 3: -4, -6, -3.

3. 2.

   Noah finds A − B one cell at a time. What is the entry in row 2, column 3 of A − B?

   10
4. 3.

   Row 1: -6, -5; row 2: 12, -8. Matrix B: row 1: 5, 5; row 2: -3, 7. Pia checks row 2, column 1 of A − B. What is that entry?

   15
5. 4.

   Row 1: 4, 1, 4; row 2: 1, 4, 1. Matrix A lists the cups of nuts, raisins and pretzels in Tala's two trail mixes. Tala makes 3 batches of each. Which matrix is 3A?

   • rows (7, 4, 7) and (4, 7, 4)
   • rows (12, 1, 4) and (1, 4, 1), one entry scaled
   • rows (12, 3, 12) and (3, 12, 3)
6. 5.

   Row 1: 2, 7; row 2: 6, 5. Matrix A gives the spoons of each paint in Zee's two color mixes. Zee doubles both mixes. Which matrix is 2A?

   • rows (4, 7) and (6, 5)
   • rows (4, 14) and (12, 10)
   • rows (4, 9) and (8, 7), scalar added
7. 6.

   Row 1: -6, -3; row 2: 2, 2. Bo multiplies every entry of matrix A by 4. Which matrix is 4A?

   • rows (-24, -3) and (2, 2)
   • rows (-24, -12) and (8, 8)
   • rows (-2, 1) and (6, 6)
   • rows (24, 12) and (8, 8)
8. 7.

   Row 1: 8, 7; row 2: 8, 2. Matrix B: row 1: -5, -2, -4; row 2: -1, 6, -3. Noah's worksheet asks for A + B. What is A + B?

   • Undefined: A and B are different sizes
   • rows (3, 5, -4) and (7, 8, -3), missing entry taken as zero
   • rows (3, 5) and (7, 8)

9. Matrix A

   Row 1: 3, 6, 7; row 2: 1, 2, 1. Matrix B: row 1: 2, -5, 8; row 2: -8, 6, 9.

10. 8.

    Pia tries to add matrices A and B. What is A + B?

    • rows (5, 11, 15) and (9, 8, 10)
    • rows (5, 1, 15) and (-7, 8, 10)
    • Undefined: A and B are different sizes

11. Matrix A

    Row 1: 8, -7; row 2: 6, -3; row 3: 8, 6. Matrix B: row 1: -5, -6; row 2: -4, 1.

12. 9.

    What is A + B for the two matrices on Ren's card?

    • Undefined: A and B are different sizes
    • rows (3, -13) and (2, -2)
    • rows (3, -13), (2, -2) and (8, 6)

13. Matrix A

    Row 1: -1, 9; row 2: -1, 2; row 3: -4, -8. Matrix B: row 1: -1, 6; row 2: -8, -1; row 3: 6, 7.

14. 10.

    Tala checks the sizes first, then adds. What is A + B?

    • rows (0, 15), (7, 3) and (2, -1)
    • rows (-2, 15), (-9, 1) and (2, -1)
    • Undefined: A and B are different sizes