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?

  • A16−32−2
  • B16−62−4
  • C64914
  • D8−31−2
  • E10−131

Q2:

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

  • A𝑎=−1, 𝑏=3, 𝑐=−1
  • B𝑎=1, 𝑏=2, 𝑐=1
  • C𝑎=1, 𝑏=−2, 𝑐=1
  • D𝑎=1, 𝑏=3, 𝑐=1
  • E𝑎=−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−2𝐴𝑍
  • B5𝐴
  • C2𝐴
  • D2𝑍𝐴
  • E−3𝑍

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−17
  • B125
  • C17
  • D116
  • E−116

Q6:

If 𝐴=[2], what is 3𝐴?

  • A2
  • B[9]
  • C2
  • D6
  • E[6]

Q7:

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

  • A[18−9]
  • B[118]
  • C[18−1]
  • D[2−9]

Q8:

If 𝐴=[8−31], what is 0𝐴?

  • A[000]
  • B[0−30]
  • C[001]
  • D[8−31]
  • E0

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[4]
  • B[−464]
  • C[−234]
  • D3−1866−12−3−9213
  • E[44−16]

Q10:

Consider the matrix equation 819−3=𝑚302−1+−1130 Find the value of 𝑚 that solves this equation.

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