Row Matrix

Q. A matrix having many rows and one column is known as

1. Row matrix
2. Column matrix
3. Diagonal matrix
4. Square matrix

Q. If a matrix has $7$ elements, then the possible number of such matrices are

Q. If $\left[\begin{array}{ccc}x+3& z+4& 2y-7\\ -6& a-1& 0\\ b-3& -21& 0\end{array}\right]=\left[\begin{array}{ccc}0& 6& 3y-2\\ -6& -3& 2c+2\\ 2b+4& -21& 0\end{array}\right]$
Find the values of $a,b,c,x,y\text{and}z$.

Q. Which of the following is an upper triangular matrix?

1. $\left[\begin{array}{ccc}5& 3& 2\\ 9& 4& 11\\ 2& -23& -7\end{array}\right]$
2. $\left[\begin{array}{ccc}5& 3& 2\\ 0& -5& 6\\ 0& 0& 5\end{array}\right]$
3. $\left[\begin{array}{ccc}-1& 4& 7\\ 0& 5& -8\\ 3& 0& 8\end{array}\right]$
4. $\left[\begin{array}{ccc}5& 0& 0\\ 3.5& 1& 0\\ -7& 6& 3\end{array}\right]$

Q. If $A$ is a square matrix of order 4, then $\text{adj(adj}A)=$ ______

Q. Let $A$ be a square matrix of order $3\times 3$, then $|5A|=$

1. $25|A|$
2. $125|A|$
3. $5|A|$
4. $15|A|$

Q. Let $A=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right],B=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right],C=\left[\begin{array}{cc}-2& 5\\ 3& 4\end{array}\right],$ then find
$\left(i\right)$ $A+B$
$\left(ii\right)$ $A-B$
$\left(iii\right)$ $3A-C$
$\left(iv\right)$ $AB$
$\left(v\right)$ $BA$

Q. Which of the following is a lower triangular matrix

1. $\left[\begin{array}{ccc}5& 3& 2\\ 9& 4& 11\\ 2& -23& -7\end{array}\right]$
2. $\left[\begin{array}{ccc}5& 3& 2\\ 0& -5& 2.6\\ 0& 0& 5\end{array}\right]$
3. $\left[\begin{array}{ccc}-1& 0.4& 1.7\\ 0& 5& -8\\ 3& 0& -1.8\end{array}\right]$
4. $\left[\begin{array}{ccc}5& 0& 0\\ 3.5& 1& 0\\ -7& 6& 3\end{array}\right]$

Q. If $2\left[\begin{array}{cc}x& 5\\ 7& y-3\end{array}\right]+\left[\begin{array}{cc}3& -4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right],$ then $(x,y)$ is

1. $(2,6)$
2. $(1,6)$
3. $(2,9)$
4. $(3,6)$

Q. If $A^{\prime }=\left[\begin{array}{cc}3& 4\\ -1& 2\\ 0& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}-1& 2& 1\\ 1& 2& 3\end{array}\right],$ then verify that:
$\left(i\right)$ $(A+B{)}^{\prime }=A^{\prime }+B^{\prime }$
$\left(ii\right)$ $(A-B{)}^{\prime }=A^{\prime }-B^{\prime }$

Q. Given an example of
(i) a row matrix which is also a column matrix,
(ii) a diagonal matrix which is not scalar,
(iii) a triangular matrix

Q. If $X+Y=\left[\begin{array}{cc}5& 2\\ 0& 9\end{array}\right]$ and $X-Y=\left[\begin{array}{cc}3& 6\\ 0& -1\end{array}\right],$ then

1. $X=\left[\begin{array}{cc}4& 4\\ 0& 4\end{array}\right]$
2. $X=\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$
3. $Y=\left[\begin{array}{cc}1& -2\\ 0& 5\end{array}\right]$
4. $Y=\left[\begin{array}{cc}-2& 1\\ 0& 5\end{array}\right]$

Q. If $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 1& 0\end{array}\right],B=\left[\begin{array}{ccc}1& 0& 0\\ 0& 3& 0\\ 0& 4& 5\end{array}\right]$, $Tr\left(BA\right)$=______

1. $40$
2. $45$
3. $39$
4. $5$

Q. Let $N=3^5\times 5^4\times 6^9\times 7^7.$ The number of factors of $N$ which are perfect squares is

1. $168$
2. $180$
3. $210$
4. $480$

Q. If $A=\left[\begin{array}{ccc}-1& 0& 2\\ 3& 1& 4\end{array}\right],B=\left[\begin{array}{ccc}0& -2& 5\\ 1& -3& 1\end{array}\right]$ and $C=\left[\begin{array}{ccc}1& -5& -2\\ 6& 0& -4\end{array}\right],$ then $2A-3B+4C$ is

1. $\left[\begin{array}{ccc}2& -14& -19\\ 27& 11& -11\end{array}\right]$
2. $\left[\begin{array}{ccc}2& 11& -19\\ -14& 11& -11\end{array}\right]$
3. $\left[\begin{array}{ccc}2& -14& -19\\ 11& 17& -11\end{array}\right]$
4. $\left[\begin{array}{ccc}-14& -14& -2\\ 17& 11& -11\end{array}\right]$

Q. If $A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& -1& 3\\ -1& 0& 2\end{array}\right]$, then $2A-B$ is

1. $\left[\begin{array}{ccc}3& 5& 3\\ -5& 6& 0\end{array}\right]$
2. $\left[\begin{array}{ccc}-5& 5& 3\\ 5& 6& 0\end{array}\right]$
3. $\left[\begin{array}{ccc}-1& 5& 3\\ 5& 6& 0\end{array}\right]$
4. $\left[\begin{array}{ccc}-1& -1& 3\\ 5& 6& 0\end{array}\right]$

Q. For all real numbers $x,y$ and $z$, the determinant
$\left|\begin{array}{ccc}2x& xy-xz& y\\ 2x+z+1& -xy-xz+yz-z^2& 1+y\\ 3x+1& 2xy-2xz& 1+y\end{array}\right|$ is equal to:

1. $(x-y)(y-z)(z-x)$
2. $(x-yz)(y-z)$
3. $(y-xz)(z-x)$
4. $zero$

Q. If $\left[\begin{array}{ccc}1& 2& 4\\ -1& 0& 9\end{array}\right]+A=\left[\begin{array}{ccc}9& -1& 1\\ 4& -2& 3\end{array}\right],$ then $A$ is

1. $\left[\begin{array}{ccc}3& -8& -3\\ 5& -2& -6\end{array}\right]$
2. $\left[\begin{array}{ccc}8& -3& -3\\ 5& -2& -6\end{array}\right]$
3. $\left[\begin{array}{ccc}10& -1& -3\\ 6& -2& -6\end{array}\right]$
4. $\left[\begin{array}{ccc}6& -3& -3\\ 10& -2& -6\end{array}\right]$

Q. If the order of the matrix is $1\times 2$, then it is a

1. Column matrix
2. Square matrix
3. None of these
4. Row matrix

Q. If $A=\left[\begin{array}{ccc}1& 1& 1\end{array}\right]$, then $A$ is a

1. Identity matrix
2. Null matrix
3. Diagonal matrix
4. Row matrix

Q.

Which among the following can always represent a vector?

1. A diagonal matrix

2. an Identity matrix

3. a scalar matrix

4. a row matrix

Q. A matrix consists of $20$ elements, what are possible it can have

Q.

Which of the following is a row matrix?

1. $\left[\begin{array}{cc}1& 2\end{array}\right]$

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

3. $\left[\begin{array}{c}5\\ 5\\ 5\end{array}\right]$

4. $\left[\begin{array}{cc}5& 1\\ 1& 5\end{array}\right]$

Q. Match the following-

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

Q.

Which of the following is a row matrix?

1. $\left[\begin{array}{cc}1& 2\end{array}\right]$

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

3. $\left[\begin{array}{c}5\\ 5\\ 5\end{array}\right]$

4. $\left[\begin{array}{cc}5& 1\\ 1& 5\end{array}\right]$

Q. Let $A=\{0,1\}$ and $N$ the set of all natural numbers. Then the mapping $f:N\to A$ defined by $f(2n-1)=0,f\left(2n\right)=1$ for all $n\in N$, is many-one onto.

1. True
2. False

Q.

Which among the following can always represent a vector?

1. A diagonal matrix

2. an Identity matrix

3. a scalar matrix

4. a row matrix