Lesson Worksheet: Matrix Multiplication Mathematics • 10th Grade

In this worksheet, we will practice identifying the conditions for matrix multiplication and evaluating the product of two matrices if possible.

Q1:

Fill in the blank: If matrix 𝐴 is of order 2Γ—3 and matrix 𝐴𝐡 is of order 2Γ—1, then matrix 𝐡 is of order .

  • A3Γ—1
  • B2Γ—1
  • C1Γ—3
  • D1Γ—2

Q2:

Given that 𝐴 is a matrix of order π‘šΓ—π‘›, and 𝐡 is a matrix of order π‘ŸΓ—π‘™, determine the condition under which 𝐴𝐡 is defined.

  • Aπ‘š=𝑛
  • Bπ‘šβ‰ π‘›
  • Cπ‘Ÿ=𝑙
  • Dπ‘›β‰ π‘Ÿ
  • E𝑛=π‘Ÿ

Q3:

Consider the matrices 𝐴=11βˆ’2βˆ’4477,𝐡=ο”βˆ’8βˆ’96βˆ’489. Find 𝐴𝐡, if possible.

  • Aο˜βˆ’8016βˆ’84βˆ’11568βˆ’74812105
  • Bο”βˆ’88364283263
  • Cο˜βˆ’88836324263
  • Dο˜βˆ’80βˆ’11548166812βˆ’84βˆ’7105
  • EIt is not possible.

Q4:

Given that 𝐴=ο”βˆ’3βˆ’7βˆ’1341,𝐡=6βˆ’43, find 𝐴𝐡 if possible.

  • A75
  • B[75]
  • Cο˜βˆ’181828βˆ’16βˆ’33
  • Dit is not possible
  • Eο”βˆ’1828βˆ’318βˆ’163

Q5:

Consider the matrices 𝐴=[12βˆ’7],𝐡=ο˜βˆ’46βˆ’2. Find 𝐴𝐡, if possible.

  • A[30]
  • B[βˆ’41214]
  • C[22]
  • Dο˜βˆ’41214

Q6:

Fill in the blank: If 𝐴 is a matrix of order 2Γ—3 and 𝐡 is a matrix of order 1Γ—3, then matrix 𝐴𝐡 is of order .

  • A2Γ—1
  • B1Γ—2
  • C3Γ—2
  • D3Γ—1

Q7:

Suppose 𝐴=11βˆ’10βˆ’21,𝐡=ο”βˆ’21βˆ’30,𝐢=0βˆ’23110.and Which of the following products is defined?

  • A𝐡𝐢
  • B𝐢
  • C𝐴
  • D𝐴𝐡
  • E𝐡𝐴

Q8:

Given that 𝐴=512βˆ’3βˆ’4βˆ’3𝐡=1βˆ’25βˆ’4,, determine 𝐴𝐡 if possible.

  • A10βˆ’14βˆ’2322
  • Bundefined
  • C10βˆ’23βˆ’1422
  • D5βˆ’22βˆ’1516βˆ’3

Q9:

Given that 𝐴=ο”βˆ’5βˆ’650, find 𝐴+5𝐴+30𝐼.

  • A66βˆ’55055
  • B0000
  • C030300
  • D1001

Q10:

The table below shows the number of different types of rooms in three hotels owned by a company. If a single room costs 160 LE per night, a double room costs 430 LE per night, and a suite costs 740 LE per night, determine the company’s daily income when all the rooms are occupied.

HotelSingle RoomDouble RoomSuite
First Hotel 45 74 15
Second Hotel 48 74 19
Third Hotel 49 94 10

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