Matrix Definition and Representation

Q. If a matrix has $18$ elements, what are the possible orders it can have? What, if the has $5$ elements?

Q. If a matrix has $24$ elements, what are the possible orders it can have? What, if it has $13$ elements?

Q. Find matrix $A$ such that$\left(\begin{array}{cc}2& -1\\ 1& 0\\ -3& 4\end{array}\right)A=\left(\begin{array}{cc}-1& -8\\ 1& -2\\ 9& 22\end{array}\right)$

Q.

If a matrix $A$is of order $3\times 2$ and matrix $B$ is of order $2\times 2$ then the matrix $AB$ is of order?

Q.

Find two consecutive positive integers, sum of whose squares is $365$.

Q. If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

Q. The number of all possible matrices of order $3\times 3$ with each entry $0$ or $1$ is:

1. $27$
2. $18$
3. $81$
4. $512$

Q.

If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?

Q. Consider two families $A$ and $B.$ Suppose there are $4$ men, $4$ women and $4$ children in family $A$ and $2$ men, $2$ women and $2$ children in family $B.$ The recommended daily amount of calories is $2400$ for a man, $1900$ for a woman, $1800$ for a child and $45$ grams of proteins for a man, $55$ grams for a woman and $33$ grams for a child.
The requirement of calories and proteins for each person is given by matrix $R$ and the number of family members in each family is given by matrix $F.$

Requirement of proteins of family $B$ is

1. $560$ grams
2. $332$ grams
3. $266$ grams
4. $532$ grams

Q.

Minimize Z = x + 2y, subject to constraints are 2x + y $\ge$ 3, x + 2y $\ge$ 6 and x, y $\ge$ 0. Show that the minimum of Z occurs at more than two points.

Q.

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

Q.

How do you Compare Two Matrices?

Q.

$25$ people for program $A,50$ people for program $B,10$ people for both. So, the number of employees employed only for $A$ is

1. $15$

2. $20$

3. $35$

4. $40$

Q. Find the number of all possible matrices of order $3\times 3$ with each entry $0$ and $1$.

Q. The number of different possible orders of matrices having $18$ elements and all are identical is:

1. $3$
2. $1$
3. $6$
4. $4$

Q. If $2X-3Y=\left[\begin{array}{cc}3& 2\\ 1& 0\end{array}\right]$ and $X+2Y=\left[\begin{array}{cc}0& 1\\ 2& 3\end{array}\right]$, and $kX=\left[\begin{array}{cc}6& 7\\ 8& 9\end{array}\right],$ then the value of $k$ is

Q. The adjoint of the matrix
$A=\left[\begin{array}{ccc}1& 1& 1\\ 2& 1& -3\\ -1& 2& 3\end{array}\right]$ is:

1. $\left[\begin{array}{ccc}9& 1& 4\\ -3& 4& 5\\ 5& -3& -1\end{array}\right]$
2. $\left[\begin{array}{ccc}9& -1& -4\\ 3& 4& 5\\ 5& 3& -1\end{array}\right]$
3. $\left[\begin{array}{ccc}-9& -1& -4\\ -3& -4& 5\\ 5& -3& -1\end{array}\right]$
4. $\left[\begin{array}{ccc}9& -1& -4\\ -3& 4& 5\\ 5& -3& -1\end{array}\right]$

Q. In the matrix , write: (i) The order of the matrix (ii) The number of elements, (iii) Write the elements a 13 , a 21 , a 33 , a 24 , a 23

Q. 10. The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is:(A) 27(B) 18(C) 81(D) 512

Q. Construct a $3\times 2$ matrix whose elements are given by $a_{ij}=\frac{1}{2}|i-3j|.$

Q. If a matrix has $18$ elements , what are the possible orders it can have? what, if it has $5$ elements?

Q.

Find the transpose of the following matrix.
$$\left[\begin{array}{ccc}-1& 5& 6\\ \sqrt{3}& 5& 6\\ 2& 3& -1\end{array}\right]$$

Q. If $\left[\begin{array}{ccc}2& 1& 3\end{array}\right]\left[\begin{array}{ccc}-1& 0& -1\\ -1& 1& 0\\ 0& 1& 1\end{array}\right]\left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]=A$, then write the order of matrix A.

Q. Let $p$ be an odd prime number and $T_p$ be the following set of $2\times 2$ matrices $T_P=\{A=\left[\begin{array}{cc}a& b\\ c& a\end{array}\right]:a,b,c\in \{0,1,2....p-1\}\}$

1. Option a
2. Option d
3. Option b
4. Option c

Q.

If element of matrix $A={\left[a_{ij}\right]}_{(3\times 3)}$ where

$A=\left\{\begin{array}{ll}{(-1)}^{j-i}& i<j\\ 2& i=j\\ {(-1)}^{i+j}& i>j\end{array}\right.$

, then the value of $|3adj(2A^{-1}\left)\right|$is:

1. $72$

2. $36$

3. $108$

4. $48$

Q. Consider two families $A$ and $B.$ Suppose there are $4$ men, $4$ women and $4$ children in family $A$ and $2$ men, $2$ women and $2$ children in family $B.$ The recommended daily amount of calories is $2400$ for a man, $1900$ for a woman, $1800$ for a child and $45$ grams of proteins for a man, $55$ grams for a woman and $33$ grams for a child.
The requirement of calories and proteins for each person is given by matrix $R$ and the number of family members in each family is given by matrix $F.$

Requirement of calories of family $A$ is

1. $24000$
2. $24400$
3. $15000$
4. $15800$

Q.

$(1+i)(2+ai)+(2+3i)(3+i)=x+iy,x,ybelongstoRandxequaly,thenaequal$

1. $5$

2. $-4$

3. $-5$

4. $4$

Q. If a matrix has $5$ elements, what are the possible orders it can have?

Q. If a matrix has 8 elements, what are the possible number of orders it can have?

Q. Construct a $3\times 4$ matrix, whose elements are given by :
$\left(i\right)$ $a_{ij}=\frac{1}{2}|-3i+j|$
$\left(ii\right)$ $a_{ij}=2i-j$