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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-15-ADD-01
Matrix Addition & Scalar Multiplication — Assignment
Chapter: Matrices
Topic: Addition and Subtraction of Matrices and Multiplication by a Scalar
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.
Matrices are added:
  • A.row by column
  • B.element by element
  • C.by determinants
  • D.by transposing
2.
Scalar multiplication multiplies:
  • A.the diagonal
  • B.every element
  • C.the first row
  • D.nothing
3.
$2\begin{bmatrix}1&2\\3&4\end{bmatrix}=$
  • A.$\begin{bmatrix}2&4\\6&8\end{bmatrix}$
  • B.$\begin{bmatrix}2&2\\2&2\end{bmatrix}$
  • C.$\begin{bmatrix}1&2\\3&4\end{bmatrix}$
  • D.$\begin{bmatrix}3&4\\5&6\end{bmatrix}$
4.
$A-A=$
  • A.$A$
  • B.zero matrix
  • C.$2A$
  • D.identity
5.
Matrix addition is:
  • A.not commutative
  • B.commutative
  • C.undefined
  • D.a product
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find $\begin{bmatrix}1&2\end{bmatrix}+\begin{bmatrix}3&4\end{bmatrix}$.
7.
Find $3\begin{bmatrix}1&0\\0&1\end{bmatrix}$.
8.
Find $\begin{bmatrix}5&6\end{bmatrix}-\begin{bmatrix}2&1\end{bmatrix}$.
9.
Find $A+O$ where $O$ is the zero matrix.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
If $A=\begin{bmatrix}1&2\\3&4\end{bmatrix},\ B=\begin{bmatrix}0&1\\1&0\end{bmatrix}$, find $A+B$.
11.
For the same $A,B$, find $2A-B$.
12.
Find $A$ if $A+\begin{bmatrix}1&1\\1&1\end{bmatrix}=\begin{bmatrix}3&2\\4&5\end{bmatrix}$.
13.
Find $3\begin{bmatrix}1&-1\\2&0\end{bmatrix}$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
If $A=\begin{bmatrix}2&3\\1&4\end{bmatrix}$ and $B=\begin{bmatrix}1&0\\2&5\end{bmatrix}$, find $2A-3B$.
15.
Find $X$ if $2X+\begin{bmatrix}1&2\\3&4\end{bmatrix}=\begin{bmatrix}5&6\\7&8\end{bmatrix}$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) element by element
  2. (B) every element
  3. (A) $\begin{bmatrix}2&4\\6&8\end{bmatrix}$
  4. (B) zero matrix
  5. (B) commutative
Section B — Short Answer (2 marks)
  1. $\begin{bmatrix}4&6\end{bmatrix}$.
  2. $\begin{bmatrix}3&0\\0&3\end{bmatrix}$.
  3. $\begin{bmatrix}3&5\end{bmatrix}$.
  4. $A$.
Section C — Short Answer (3 marks)
  1. $\begin{bmatrix}1&3\\4&4\end{bmatrix}$.
  2. $\begin{bmatrix}2&3\\5&8\end{bmatrix}$.
  3. $\begin{bmatrix}2&1\\3&4\end{bmatrix}$.
  4. $\begin{bmatrix}3&-3\\6&0\end{bmatrix}$.
Section D — Long Answer (5 marks)
  1. $\begin{bmatrix}1&6\\-4&-7\end{bmatrix}$.
  2. $\begin{bmatrix}2&2\\2&2\end{bmatrix}$.
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