# Matrix Definition and Representation

## Trending Questions

**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⎛⎜⎝2−110−34⎞⎟⎠A=⎛⎜⎝−1−81−2922⎞⎟⎠

**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 3×3 with each entry 0 or 1 is:

- 27
- 18
- 81
- 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

- 560 grams
- 332 grams
- 266 grams
- 532 grams

**Q.**

Minimize Z = x + 2y, subject to constraints are 2x + y ≥ 3, x + 2y ≥ 6 and x, y ≥ 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

$15$

$20$

$35$

$40$

**Q.**Find the number of all possible matrices of order 3×3 with each entry 0 and 1.

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

- 3
- 1
- 6
- 4

**Q.**If 2X−3Y=[3210] and X+2Y=[0123], and kX=[6789], then the value of k is

**Q.**The adjoint of the matrix

A=⎡⎢⎣11121−3−123⎤⎥⎦ is:

- ⎡⎢⎣914−3455−3−1⎤⎥⎦
- ⎡⎢⎣9−1−434553−1⎤⎥⎦
- ⎡⎢⎣−9−1−4−3−455−3−1⎤⎥⎦
- ⎡⎢⎣9−1−4−3455−3−1⎤⎥⎦

**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 3×2 matrix whose elements are given by aij=12|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.

⎡⎢⎣−156√35623−1⎤⎥⎦

**Q.**If [213]⎡⎢⎣−10−1−110011⎤⎥⎦⎡⎢⎣10−1⎤⎥⎦=A, then write the order of matrix A.

**Q.**Let p be an odd prime number and Tp be the following set of 2×2 matrices TP={A=[abca]:a, b, c∈{0, 1, 2....p−1}}

- Option a
- Option d
- Option b
- 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 $|3adj(2{A}^{-1}\left)\right|$is:

$72$

$36$

$108$

$48$

**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

- 24000
- 24400
- 15000
- 15800

**Q.**

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

$5$

$-4$

$-5$

$4$

**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 3×4 matrix, whose elements are given by :

(i) aij=12|−3i+j|

(ii) aij=2i−j