Lesson Worksheet: Operations with Matrices Mathematics

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In this worksheet, we will practice adding and subtracting matrices and multiplying them by a constant, which is called scalar multiplication of a matrix.

Q1:

Given that −𝑋−𝑌=08−6−3,𝑋−𝑌=−6−16019, what are 𝑋 and 𝑌?

  • A𝑋=−3−12311, 𝑌=343−8
  • B𝑋=−6−24622, 𝑌=121−4
  • C𝑋=−6−8−616, 𝑌=0−863
  • D𝑋=−6−24622, 𝑌=08−6−3

Q2:

Consider the matrix 𝐴=−1−1513−10. Suppose the sum of matrices 𝐴 and 𝐵 is 𝐴+𝐵=10−1012. Find the matrix 𝐵.

  • A0−1−61302
  • B−2−16−1322
  • C21−6−1322
  • D0−141302
  • E−2−1613−2−2

Q3:

Find [12−1]+[282].

  • A1103
  • B[3103]
  • C[3101]
  • D[1103]
  • E3101

Q4:

Given that 𝑋=−3−215−8−8,𝑌=−18−9−97−2,𝑍=3−8−70−85, what is the matrix 3𝑋+𝑌−3𝑍?

  • A−1−22−276−41−11
  • B−19−115−37−4
  • C0−1−14−3−8−4
  • D−19261567−41

Q5:

Evaluate 811−37+10−131.

  • A2110108
  • B1810−68
  • C187−3−2
  • D181008
  • E18−4148

Q6:

Solve for matrix 𝑋 in the matrix equation 3𝑋+𝐵=𝐶, where 𝐵 and 𝐶 are 𝐵=57−10−8,𝐶=8−227.

  • A3−91215
  • B6−61518
  • C−13−4−5
  • D1−345
  • E0−12−11−4

Q7:

Suppose the sum 𝐴+𝐵+𝐶 exists. We also know that 𝐴 has 2 rows and 𝐶 has 3 columns. What can we say about matrix 𝐵?

  • A𝐵 is a 1×3 matrix.
  • B𝐵 is a 3×2 matrix.
  • C𝐵 is a 3×3 matrix.
  • D𝐵 is a 2×3 matrix.
  • E𝐵 is a 2×2 matrix.

Q8:

Find 79−50−8−520.

  • A−114−30
  • B154−30
  • C−114−70
  • D151470

Q9:

Given that both 𝐴 and 𝐵 have the order 1×2, determine the order of the matrix 6𝐴−6𝐵.

  • A1×2
  • B2×1
  • C6×12
  • D6×6

Q10:

If the matrix 𝐴 is added to a zero matrix of the same size, is the result equal to matrix 𝐴?

  • AYes
  • BNo

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