Question 1, Review Exercise

Solutions of Question 1 of Review Exercise of Unit 02: Matrices and Determinants. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Select the best matching option. Chose the correct option.

i. If order of $A$ is $m \times n$ and order of $B$ is $n \times p$ then order of $A B$ is:

• (a) $n \times p$
  
• (b) $m \times p$
  
• (c) $p \times m$
  
• (d) $n \times n$
  See Answer

  (b): $m \times p$

ii. If $A$ is a row matrix of order $1 \times n$ then order of $A^{t} A$ is:

• (a) $1 \times n$
  
• (b) $n \times 1$
  
• (c) $1 \times 1$
  
• (d) $n \times n$
  See Answer

  (d): $n \times n$

iii. For an element $a_{i j}$ of a square matrix $A$ :

• (a) $a_{i j}=(-1)^{i+j} A_{i j}$
  
• (b)$a_{i j}=(-1)^{i+j} M_{i j}$
  
• (c) $\frac{A_{i j}}{M_{i j}}=(-1)^{i+j}$
  
• (d) $a_{i j}=M_{i j}$
  See Answer

  (d): $a_{i j}=M_{i j}$

iv. If $A$ is any matrix then $A$ and $A^{t}$ are always conformable for:

• (a) addition
  
• (b) multiplication
  
• (c) subtraction
  
• (d) all of these
  See Answer

  (b): multiplication

v. If $A$ is a square matrix of order $3 \times 3$ and $|A|=3$ then value of $|\operatorname{adj} A|$ is:

• (a) $3$
• (b) $1 / 3$
• (c) $9$
• (d) $6$
  See Answer

  ©: $9$

vi. For the square matrix $A$ of order $3 \times 3$ with $|A|=9 ; A_{21}=2 ; A_{22}=3 ; A_{23}=-1$; $a_{21}=1 ; a_{23}=2$, the value of $a_{22}$ is:

• (a) $2$
• (b) $3$
• (c) $9$
• (d) $-1$
  See Answer

  (b): $3$

vii. System of homogeneous linear equations has non-trivial solution if:

• (a) $|A|>0$
• (b) $|A|<0$
• (c) $|A|=0$
• (d) $|A| \neq 0$
  See Answer

  (d): $|A| \neq 0$

viii. For non-homogeneous system of equations; the system is inconsistent if:

• (a) $\operatorname{RankA}=\operatorname{Rank} A_{b}$$
• (b) $\operatorname{RankA} \neq \operatorname{Rank} A_{b}$
• (c) RankA < no. of variables
• (d) Rank $A_{b}>$ no. of variables
  See Answer

  (c): RankA < no. of variables

ix. For a system of non-homogeneous equations with three variables system will have unique solution if:

• (a) $\operatorname{RankA}<3$
• (b) $\operatorname{Rank} A_{b}<3$
• (c) $\operatorname{RankA}=\operatorname{RankA}_{b}=3$
• (d) $\operatorname{Rank} A=\operatorname{Rank} A_{b}<3$
  See Answer

  (c):$\operatorname{RankA}=\operatorname{RankA}_{b}=3$

x. A system of non- homogeneous equation having infinite many solutions can be solved by using:

• (a) Inversion method
• (b) Cramer's rule
• (c) Gauss-Jordan method
• (d) all of these
  See Answer

  (d): all of these

Question 2 &3 >