====== 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. 

=====Question 1=====
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) $n \times n$ \\ <btn type="link" collapse="a1">See Answer</btn><collapse id="a1" collapsed="true">%%(b)%%: $m \times p$</collapse>

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) $n \times n$  \\ <btn type="link" collapse="a2">See Answer</btn><collapse id="a2" collapsed="true">(d): $n \times n$</collapse>

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) $a_{i j}=M_{i j}$  \\ <btn type="link" collapse="a3">See Answer</btn><collapse id="a3" collapsed="true">(d): $a_{i j}=M_{i j}$</collapse>

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 \\ <btn type="link" collapse="a4">See Answer</btn><collapse id="a4" collapsed="true">(b): multiplication </collapse>

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) $6$ \\ <btn type="link" collapse="a5">See Answer</btn><collapse id="a5" collapsed="true">(c): $9$</collapse>

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) $-1$ \\ <btn type="link" collapse="a6">See Answer</btn><collapse id="a6" collapsed="true">(b): $3$</collapse>

vii. System of homogeneous linear equations has non-trivial solution if: 
    * (a) $|A|>0$  
    * (b) $|A|<0$
    * %%(c)%% $|A|=0$ 
    * (d) $|A| \neq 0$ \\ <btn type="link" collapse="a7">See Answer</btn><collapse id="a7" collapsed="true">%%(d)%%: $|A| \neq 0$</collapse>

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 \\ <btn type="link" collapse="a8">See Answer</btn><collapse id="a8" collapsed="true">%%(c)%%: RankA < no. of variables</collapse>

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) $\operatorname{Rank} A=\operatorname{Rank} A_{b}<3$ \\ <btn type="link" collapse="a9">See Answer</btn><collapse id="a9" collapsed="true">%%(c)%%:$\operatorname{RankA}=\operatorname{RankA}_{b}=3$</collapse>

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 \\ <btn type="link" collapse="a10">See Answer</btn><collapse id="a10" collapsed="true">%%(d)%%: all of these</collapse>




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<text align="right"><btn type="success">[[math-11-nbf:sol:unit02:Re-ex-p2|Question 2 &3 >]]</btn></text>