Matrix Definition and Representation

Q.

$2\surd 3+\surd 3$ is equals to ?

1. $2\surd 6$

2. $6$

3. $3\surd 3$

4. ​$4\surd 6$

Q.

Construct a $3\times 3$ matrix whose elements $a_{ij}$ are given by $a_{ij}=0$ if $i<j$ and $a_{ij}=i+j$ if $i\ge j$.

1. $\left(\begin{array}{ccc}4& 5& 6\\ 0& 3& 4\\ 0& 0& 2\end{array}\right)$

2. $\left(\begin{array}{ccc}4& 5& 6\\ 3& 4& 0\\ 2& 0& 0\end{array}\right)$

3. $\left(\begin{array}{ccc}2& 0& 0\\ 3& 4& 0\\ 4& 5& 6\end{array}\right)$

4. $\left(\begin{array}{ccc}0& 0& 0\\ 1& 2& 3\\ 4& 5& 0\end{array}\right)$

Q.

If a matrix has 8 elements, how many possible orders can it have?

1. 1

2. 2

3. 4

4. 5

Q. Construct a $3\times 4$ matrix whose elements $a_{ij}$ are given by $a_{ij}=i+2j$

Q.

If a matrix has 15 elements, what are the possible orders it can have?

Q.

If the number of rows and columns of a matrix are not equal, then the matrix is called ___ matrix.

Q.

If a matrix has 15 elements, how many possible orders can it have?

___

Q.

Marko currently has $20$ tulips in his yard.

Each year he plants $5$ more.
Write a recursive formula for the number of tulips Marko has.

Q.

Construct a 2 $\times$ 2 matrix by A = $\left[a_{ij}\right]$ whose elements are given by $a_{ij}$= 2i – j

Q. What can be the general notation of a matrix with 4 rows and 5 columns?

1. 5x4
2. 4x5
3. 4x4
4. 5x5

Q. Construct a $3\times 3$ matrix whose elements $a_{ij}$ are given by $a_{ij}=0$ if $i\ne j$ and $a_{ij}=i\times j$ if $i=j$

Q. Construct a $3\times 3$ matrix whose elements $a_{ij}$ are given by $a_{ij}=0$ if $i<j$ and $a_{ij}=i+j$ if $i\ge j$.

Q. How many possible orders can a matrix with 15 elements have?

1. 3
2. 6
3. 4
4. 5

Q.

If A = $(a_{ij}{)}_{2\times 2}$ , where $a_{ij}$ = i + j, then A is equal to

1. 

2. 

3. 

4. 

Q.

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

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

1. 2 x 3

2. 3 x 2

3. 1 x 2

4. 1 x 3

Q.

Let M$\times \left[\begin{array}{cc}1& 1\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}1& 2\end{array}\right]$, where M is a matrix.

State the order of the matrix M.

1. 2 × 1

2. 1 × 2

3. 2 × 2

4. 1 × 3

Q.

Identify the correct statements:

(i) A matrix with 3 columns and 2 rows is of order $3\times 2$.
(ii) A matrix with 5 columns and 8 rows is of order $8\times 5$
(iii) If the order of a matrix is $4\times 3$, then it has 12 elements.
(iv) If the order of a matrix is $5\times 3$, then it has 10 elements.

1. (i) and (ii)

2. (ii) and (iii)

3. (i) and (iii)

4. (i) and (iv)

Q. Let $A=${$1,2,3,4$} and $B=${$1,2$}. Then the number of onto functions from $A$ to $B$ is:

1. $14$
2. $12$
3. $8$
4. None of these

Q.

Explain closure, associative, multiplicative and distributive properties of multiplication of matrices.

Q.

Construct a $3\times 4$ matrix whose elements $a_{ij}$ are given by $a_{ij}=i+2j$

1. $\left[\begin{array}{cccc}1& 3& 5& 9\\ 4& 6& 8& 10\\ 5& 7& 9& 11\end{array}\right]$

2. $\left[\begin{array}{cccc}3& 5& 7& 9\\ 4& 6& 8& 10\\ 5& 7& 9& 11\end{array}\right]$

3. $\left[\begin{array}{cccc}3& 5& 7& 9\\ 2& 1& 0& 3\\ 2& 4& 6& 8\end{array}\right]$

4. $\left[\begin{array}{cccc}3& 5& 7& 9\\ 2& 1& 0& 3\\ 5& 7& 9& 11\end{array}\right]$

Q. How to find Determinant of matrix of order 33 ?

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. are the type of brackets a matrix is represented with.

1. Flower brackets
2. Round brackets
3. Square brackets

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 x 3

2. 3 x 2

3. 1 x 2

4. 1 x 3

Q.

Construct a $3\times 3$ matrix whose elements $a_{ij}$ are given by $a_{ij}=0$ if $i\ne j$ and $a_{ij}=-8$ if $i=j$.

Q.

If a matrix has 15 elements, how many possible orders can it have? ___

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

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

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

Q. is not a type of matrices.

1. Square matrix
2. Circular matrix
3. Diagonal matrix

Q. Write the matrix form for linear equations: $3x+4y=54x+5y=9$

1. $\left[\begin{array}{cc}3& 4\\ 4& 5\end{array}\right]\times \left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}5\\ 9\end{array}\right]$
2. $\left[\begin{array}{cc}4& 5\\ 3& 4\end{array}\right]\times \left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}5\\ 9\end{array}\right]$
3. $\left[\begin{array}{cc}3& 4\\ 4& 5\end{array}\right]\times \left[\begin{array}{c}y\\ x\end{array}\right]=\left[\begin{array}{c}5\\ 9\end{array}\right]$
4. $\left[\begin{array}{cc}4& 3\\ 5& 4\end{array}\right]\times \left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}5\\ 9\end{array}\right]$

Q. If $\left[a_{ij}\right]$ is an element of matrix A then it lies in row of the matrix.

1. $j^{th}$
2. $i^{th}$
3. $a^{th}$