Worksheet: Scalar Multiplication of Matrices

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In this worksheet, we will practice multiplying a scalar by a matrix and identifying the properties of their multiplication.

Q1:

Given the matrix 𝐴=8−31−2, what is 2𝐴?

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

Q2:

Find numbers 𝑎, 𝑏, and 𝑐 so that 𝑎110−1+𝑏1001+𝑐0−110=10−13.

  • A 𝑎 = − 1 , 𝑏 = 2 , 𝑐 = − 1
  • B 𝑎 = 1 , 𝑏 = 3 , 𝑐 = 1
  • C 𝑎 = − 1 , 𝑏 = 3 , 𝑐 = − 1
  • D 𝑎 = 1 , 𝑏 = − 2 , 𝑐 = 1
  • E 𝑎 = 1 , 𝑏 = 2 , 𝑐 = 1

Q3:

Given that 𝑥×−20−3−5=1402135, find the value of 𝑥.

Q4:

Let 𝑍 be a 2×3 matrix whose entries are all zero. If 𝐴 is any 2×3 matrix, which of following is equivalent to 5𝐴−3𝑍?

  • A 2 𝑍 𝐴
  • B − 2 𝐴 𝑍
  • C 2 𝐴
  • D 5 𝐴
  • E − 3 𝑍

Q5:

Given the matrix 𝐴=1−1652−4−3−174, what is the greatest number 𝑘 for which no entry of 𝑘𝐴 is greater than 1?

  • A 1 7
  • B 1 1 6
  • C − 1 1 6
  • D − 1 7
  • E 1 2 5

Q6:

If 𝐴=[2], what is 3𝐴?

  • A [ 6 ]
  • B 2
  • C 6
  • D 2
  • E[9]

Q7:

Consider the matrix 𝐴. Find 9𝐴. 𝐴=[2−1]

  • A [ 1 8 − 9 ]
  • B [ 1 1 8 ]
  • C [ 1 8 − 1 ]
  • D [ 2 − 9 ]

Q8:

If 𝐴=[8−31], what is 0𝐴?

  • A [ 0 0 1 ]
  • B 0
  • C [ 8 − 3 1 ]
  • D [ 0 0 0 ]
  • E [ 0 − 3 0 ]

Q9:

Olivia has defined the notion of a 'prime matrix' as follows. A matrix 𝐴 is a prime matrix if the following two conditions hold:

  1. It is none zeros with integers entries.
  2. If 𝐴=𝑘𝐵, then 𝑘=1 or 𝑘=−1.

Which of the following matrices are prime according to Olivia's definition?

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

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