Vidaara.orgClass 12 · Mathematics
CodeVID-M12-04-INV-01
Inverse of a Matrix & Linear Systems — Assignment
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.
$A^{-1}=$
- A.$|A|\operatorname{adj}A$
- B.$\tfrac{1}{|A|}\operatorname{adj}A$
- C.$\tfrac{1}{|A|}A^{T}$
- D.$\operatorname{adj}A$
2.
A system $AX=B$ has a unique solution when:
- A.$|A|=0$
- B.$|A|\ne0$
- C.$B=O$
- D.$A=I$
3.
The matrix $\begin{bmatrix}1&2\\2&4\end{bmatrix}$ is:
- A.invertible
- B.singular
- C.an identity
- D.symmetric and invertible
4.
If $|A|=0$ and $(\operatorname{adj}A)B\ne O$, the system is:
- A.uniquely solvable
- B.inconsistent
- C.infinitely many
- D.homogeneous
5.
$(A^{-1})^{-1}=$
- A.$A^{-1}$
- B.$A$
- C.$I$
- D.$\operatorname{adj}A$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find $|A|$ for $A=\begin{bmatrix}2&3\\1&4\end{bmatrix}$ and state whether it is invertible.
7.
Is $\begin{bmatrix}1&2\\2&4\end{bmatrix}$ invertible?
8.
Find $A^{-1}$ for $A=\begin{bmatrix}1&0\\0&2\end{bmatrix}$.
9.
Write the system $2x+3y=5,\ x-y=0$ as $AX=B$ (give $A$).
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find $A^{-1}$ for $A=\begin{bmatrix}2&3\\1&4\end{bmatrix}$.
11.
Solve $2x+3y=8,\ x+4y=9$ by the matrix method.
12.
Solve $x+y=3,\ x-y=1$ by the matrix method.
13.
Examine the consistency of $2x+y=3,\ 4x+2y=7$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Solve $x+2y=4,\ 3x+4y=10$ by the matrix method.
15.
Solve $5x+2y=4,\ 7x+3y=5$ by the matrix method.
Answer Key
Section A — Multiple Choice Questions
- (B) $\tfrac{1}{|A|}\operatorname{adj}A$
- (B) $|A|\ne0$
- (B) singular
- (B) inconsistent
- (B) $A$
Section B — Short Answer (2 marks)
- $|A|=5$; invertible.
- No (singular).
- $\begin{bmatrix}1&0\\0&\tfrac12\end{bmatrix}$.
- $A=\begin{bmatrix}2&3\\1&-1\end{bmatrix}$.
Section C — Short Answer (3 marks)
- $\tfrac15\begin{bmatrix}4&-3\\-1&2\end{bmatrix}$.
- $x=1,\ y=2$.
- $x=2,\ y=1$.
- Inconsistent (no solution).
Section D — Long Answer (5 marks)
- $x=2,\ y=1$.
- $x=2,\ y=-3$.
Generated by Vidaara.org · Assignment VID-M12-04-INV-01 · vidaara.org