Order of a Matrix

Q.

Define trace of a matrix.

Q.

What is the rank of a singular matrix?

Q.

Had Anitha scored 10 more marks in her mathematics test out of 30, 9 times these marks would have been the square of her actual marks. How many marks did she get In the test?

Q. There are 625 dots on a sheet and the number of rows is equal to the number of columns. If the number of rows is reduced by 5 and the number of columns is doubled then how many dots will be there in total?

1. 900
2. 875
3. 600
4. 1000

Q.

The rates for the entrance tickets at a water theme park are listed below

$\begin{array}{ccc}\text{Category}& \text{Weekday}& \text{Weekend}\\ & \text{price}& \text{price}\\ \text{Adults}& 400& 500\\ \text{Senior}& 200& 250\\ \text{Citizens}& & \\ \text{Children}& 300& 400\end{array}$

What is the dimension of the matrix formed by listing the weekday and weekend rates along the column of the matrix?

1. $1\times 2$

2. $1\times 3$

3. $2\times 3$

4. $3\times 2$

Q. Which constant should be added and subtracted to solve the quadratic equation $4x^2-\sqrt{3}x-5=0$ by the method of completing the square?
(a) $\frac{9}{10}$
(b) $\frac{3}{16}$
(c) $\frac{3}{4}$
(d) $\frac{\sqrt{3}}{4}$

Q.

the houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proceeding the house numbered X is equal to sum of the numbers of houses following X.

Q.

The order of matrix $A=\left[\begin{array}{ccccc}2& -2& 4& 3& 1\\ 0& 9& -3& -1& 0\\ 0& 0& 5& 0& 0\\ -2& 0& 0& -7& -1\\ -1& 0& 0& -5& 1\\ -1& -2& 0& 0& 0\end{array}\right]$ is ___

1. $6\times 5$

2. $5\times 6$

3. $6\times 6$

4. $5\times 5$

Q.

Solve thefollowing riddles, you may yourself construct such riddles.

Who am I?

(i) Goround a square

Counting every corner

Thrice and no more!

Add the count to me

To get exactly thirty four!

(ii) Foreach day of the week

Make an upcount from me

If you make no mistake

You will get twenty three!

(iii) I ama special number

Take away from me a six!

A whole cricket team

You will still be able to fix!

(iv) Tellme who I am

I shall give a pretty clue!

You will get me back

If you take me out of twenty two!

Q.

The rates for the entrance tickets at a water theme park are listed below

$\begin{array}{ccc}\text{Category}& \text{Weekday}& \text{Weekend}\\ & \text{price}& \text{price}\\ \text{Adults}& 400& 500\\ \text{Senior}& 200& 250\\ \text{Citizens}& & \\ \text{Children}& 300& 400\end{array}$

What is the dimension of the matrix formed by listing the weekday and weekend rates along the column of the matrix?

1. $2\times 3$

2. $3\times 2$

3. $1\times 2$

4. $1\times 3$

Q.

If [1 2 3] A = [4 5], the order of matrix A is

1. 3 $\times$ 2

2. 3 $\times$ 1

3. 2 $\times$ 3

4. 2 $\times$ 1

Q. 5m² + m = 3

Q. There is a group of people, some of them are creative, some are caring and the remaining 15 are optimistic. The number of caring people is twice the number of creative people. If the sum of one fourth of the square of creative people along with all the caring and optimistic ones is equal to square of the number of creative people, find (i) the total number of people in the group. (ii) how many people in the group are creative?

Q.

Identify the matrix whose order is $4\times 3$

1. $\left[\begin{array}{ccc}3& 5& 7\\ 4& 6& 8\\ 2& 4& 6\end{array}\right]$

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

3. $\left[\begin{array}{ccc}1& 2& 3\\ 4& 4& 1\\ 1& 2& 2\\ 1& 0& 4\end{array}\right]$

4. $\left[\begin{array}{cccc}1& 3& 5& 3\\ 4& 6& 8& 5\\ 5& 7& 9& 6\end{array}\right]$

Q.

The order of a column matrix can be

1. 1 $\times$ 2

2. 3 $\times$ 1

3. 2 $\times$ 2

4. 3 $\times$ 2

Q. Match the following type of matrices to their general order.

1. $A_{n\times n}$
2. $B_{1\times n}$
3. $C_{m\times 1}$