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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-15-CMP-01
Compatible Matrices — Assignment
Chapter: Matrices
Topic: Compatible Matrices
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Two matrices can be added if they have the:
  • A.same order
  • B.same rows only
  • C.product defined
  • D.same first entry
2.
For $AB$ to exist:
  • A.rows of $A$ $=$ rows of $B$
  • B.columns of $A$ $=$ rows of $B$
  • C.$A=B$
  • D.both square
3.
A $2\times3$ and a $3\times2$ matrix can be:
  • A.added
  • B.multiplied
  • C.neither
  • D.equal
4.
Addition of a $3\times2$ and a $2\times3$ matrix is:
  • A.defined
  • B.not defined
  • C.a $3\times3$
  • D.a $2\times2$
5.
Equal matrices have the same order and:
  • A.equal entries
  • B.equal sum
  • C.equal product
  • D.equal trace only
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Can a $2\times2$ and a $2\times2$ matrix be added?
7.
Can a $2\times3$ and a $3\times2$ matrix be added?
8.
Can a $2\times3$ matrix multiply a $3\times4$ matrix?
9.
Is addition of a $3\times2$ and a $2\times3$ matrix defined?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
State the condition for two matrices to be conformable for addition.
11.
State the condition for the product $AB$ to be defined.
12.
If $A$ is $2\times3$ and $B$ is $3\times5$, find the order of $AB$.
13.
Can we compute $A+B$ if $A$ is $2\times2$ and $B$ is $3\times3$?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Given $A$ of order $3\times4$ and $B$ of order $4\times3$, state the orders of $AB$ and $BA$.
15.
For $A$ ($2\times3$), $B$ ($3\times2$), $C$ ($2\times2$): which of $A+B$, $AB$, $BC$ are defined, and of what order?

Answer Key

Section A — Multiple Choice Questions
  1. (A) same order
  2. (B) columns of $A$ $=$ rows of $B$
  3. (B) multiplied
  4. (B) not defined
  5. (A) equal entries
Section B — Short Answer (2 marks)
  1. Yes.
  2. No.
  3. Yes (result $2\times4$).
  4. No.
Section C — Short Answer (3 marks)
  1. They must have the same order.
  2. Columns of $A$ $=$ rows of $B$.
  3. $2\times5$.
  4. No.
Section D — Long Answer (5 marks)
  1. $AB$ is $3\times3$; $BA$ is $4\times4$.
  2. $AB$: $2\times2$; $BC$: $3\times2$; $A+B$: not defined.
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