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Worksheet: Multiplying Matrices

In this worksheet, we will practice multiplying matrices.

Q1:

Given that find .

  • A
  • B
  • C
  • D

Q2:

Given that find .

  • A
  • B
  • C
  • D

Q3:

Given that find .

  • A
  • B
  • C
  • D

Q4:

Consider the matrices

Find 𝐴 𝐵 if possible.

  • A 2 6 4 − 9 − 1 0 − 1 6 2 8 − 4 5 − 8 1 4
  • B − 6 4 4 − 1 9 2 9 3 2 − 2 0 − 3 0 − 1 6 1 2
  • C 2 6 − 1 0 − 4 5 4 − 1 6 − 8 − 9 2 8 1 4
  • D − 6 2 9 − 3 0 4 4 3 2 − 1 6 − 1 9 − 2 0 1 2

Q5:

Consider the given matrices. Find and if possible.

  • A ,
  • B ,
  • C ,
  • D ,
  • Enot possible

Q6:

Consider the matrices

Find 𝐴 𝐵 .

  • A 𝐴 𝐵 = 𝑎 𝑏 𝑏 𝑐 𝑎 𝑏 𝑐 𝑐 𝑎
  • B 𝐴 𝐵 = 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑐 𝑐 𝑐
  • C 𝐴 𝐵 = 𝑎 𝑏 𝑐 𝑎 𝑏 𝑐 𝑎 𝑏 𝑐
  • D 𝐴 𝐵 = 𝑎 𝑏 𝑐 𝑎 𝑏 𝑐 𝑎 𝑏 𝑐
  • E 𝐴 𝐵 = 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑐 𝑐 𝑐

Find 𝐵 ′ 𝐴 ′ .

  • A 𝐵 ′ 𝐴 ′ = 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑐 𝑐 𝑐
  • B 𝐵 ′ 𝐴 ′ = 𝑎 𝑏 𝑐 𝑎 𝑏 𝑐 𝑎 𝑏 𝑐
  • C 𝐵 ′ 𝐴 ′ = 𝑎 𝑐 𝑐 𝑏 𝑎 𝑐 𝑏 𝑏 𝑎
  • D 𝐵 ′ 𝐴 ′ = 𝑎 𝑏 𝑐 𝑎 𝑏 𝑐 𝑎 𝑏 𝑐
  • E 𝐵 ′ 𝐴 ′ = 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑐 𝑐 𝑐

Q7:

Suppose

Find the product 𝐴 𝐵 .

  • A [ 1 9 ]
  • B [ 6 ]
  • C [ 1 5 ]
  • D [ 1 5 ]
  • E [ 1 9 ]

Find the product 𝐵 𝐴 .

  • A 8 − 1 6 − 2 4 1 − 2 − 3 − 3 6 9
  • B 8 − 1 6 − 2 4 1 − 2 − 3 3 − 6 − 9
  • C 8 − 1 6 − 2 4 1 − 2 − 3 3 − 6 − 9
  • D 8 1 6 2 4 1 2 3 3 6 9
  • E 8 − 1 6 − 2 4 1 − 2 − 3 − 3 6 9

Q8:

Given that find if possible.

  • A
  • B
  • C
  • D

Q9:

Given that find if possible.

  • A
  • B
  • C
  • D

Q10:

Given that find if possible.

  • A
  • B
  • C
  • D

Q11:

Given that find if possible.

  • A
  • B
  • C
  • D

Q12:

Evaluate the matrix product

  • A 8 3 8 9 2 1 − 4
  • B 8 0 − 1 1 − 9 7
  • C 1 1 0 − 8 2 1 − 3
  • D 1 1 3 3 − 9 1 0
  • E 4 7 − 1 9 − 5 1 − 4

Q13:

Consider the matrix product

What can you conclude about it?

  • A For a given 2 × 3 matrix 𝐴 , there can be a matrix 𝐵 that is not the 3 × 3 identity matrix for which 𝐴 𝐵 = 𝐵 .
  • BFor a given 2 × 3 matrix 𝐴 , there can be a matrix 𝐵 that is not the 3 × 3 identity matrix for which 𝐴 𝐵 = 𝐴 .
  • CFor a given 2 × 3 matrix 𝐴 , there cannot be any matrix 𝐵 except the 2 × 2 identity matrix for which 𝐵 𝐴 = 𝐴 .
  • DFor a given 2 × 3 matrix 𝐴 , there can be a matrix 𝐵 that is not the 2 × 2 identity matrix for which 𝐵 𝐴 = 𝐴 .

Is it possible to find a matrix 𝐵 with the above property for every 2 × 3 matrix 𝐴 ?

  • Ano
  • Byes

Q14:

Consider the matrices and . Find and .

  • A ,
  • B ,
  • C ,
  • D ,

Q15:

Let 𝑥 = [ − 1 − 1 1 ] and 𝑦 = [ 0 1 2 ] . Find 𝑥 𝑦 𝑇 and 𝑥 𝑦 𝑇 .

  • A 0 1 2 0 1 2 0 − 1 − 2 , 1
  • B 0 − 1 − 2 0 − 1 − 2 0 1 2 , − 1
  • C 0 1 2 0 1 2 0 − 1 − 2 , − 1
  • D 0 − 1 − 2 0 − 1 − 2 0 1 2 , 1
  • E 0 0 0 − 1 − 1 1 2 2 2 , 1

Q16:

Consider the matrices , , and . Find if possible.

  • A
  • B
  • C
  • D

Q17:

Given that and is the unit matrix of the same order, find the matrix for which .

Q18:

Given that find if possible.

  • A
  • B
  • C
  • D

Q19:

Given that and , find if possible.

  • A
  • B
  • C
  • D

Q20:

Given that find if possible.

  • A
  • B
  • C
  • D

Q21:

Given that find if possible.

  • A
  • B
  • C
  • D

Q22:

Consider the shown matrices and . Find if possible.

  • A
  • B
  • C
  • D

Q23:

Consider the shown matrices and . Find if possible.

  • A
  • B
  • C
  • D

Q24:

Consider the shown matrices and . Find if possible.

  • A
  • B
  • C
  • D

Q25:

Given that