Elementary Transformations

Q. Which of the following matrices can NOT be obtained from the matrix $\left[\begin{array}{cc}-1& 2\\ 1& -1\end{array}\right]$ by a single elementary row operation?

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}3& 1\\ 5& 2\end{array}\right]$, if it exists.

Q.

If A and B are two matrices, then AB is defined only if

1. No. of rows of matrix A is equal to the number of rows of matrix B.

2. No. of columns of matrix A is equal to the number of rows of matrix B.

3. No. of columns of matrix A is equal to no. of columns of matrix B.

4. No. of rows of matrix A is equal to the no. of columns of matrix B

Q. Find a matrix $A$ such that $2A-3B+5C=O,$ where $B=\left[\begin{array}{ccc}-2& 2& 0\\ 3& 1& 4\end{array}\right]\text{and}C=\left[\begin{array}{ccc}2& 0& -2\\ 7& 1& 6\end{array}\right].$

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}4& 5\\ 3& 4\end{array}\right]$, if it exists.

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{ccc}2& 0& -1\\ 5& 1& 0\\ 0& 1& 3\end{array}\right]$, if it exists.

Q. If $A=\left[\begin{array}{cc}0& \sin \alpha \\ \sin \alpha & 0\end{array}\right]$ and $det(A^2-\frac{1}{2}I)=0,$ then a possible value of $a$ is:

1. $\frac{\pi }{6}$
2. $\frac{\pi }{2}$
3. $\frac{\pi }{3}$
4. $\frac{\pi }{4}$

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}1& 3\\ 2& 7\end{array}\right]$, if it exists.

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right],$ if it exists.

Q.

The following matrix can be converted to a Identity matrix using elementary row transformations $\left[\begin{array}{ccc}1& 2& 2\\ 2& 5& 5\\ -1& 1& 1\end{array}\right]$

1. True

2. False

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}2& 5\\ 1& 3\end{array}\right]$, if it exists.

Q.

If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be ______ of A

1. Equivalent

2. Inverse

3. Adjoint

4. None of the these

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cccc}2& -3& 3& \\ 2& 2& 3& \\ 3& -2& 2& \end{array}\right]$, if it exists.

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}3& 10\\ 2& 7\end{array}\right]$, if it exists.

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}2& 1\\ 4& 2\end{array}\right]$, if it exists.

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}3& -1\\ -4& 2\end{array}\right]$, if it exists.

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}2& -6\\ 1& -2\end{array}\right]$, if it exists.

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}2& 1\\ 1& 1\end{array}\right]$, if it exists.

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}2& 3\\ 5& 7\end{array}\right]$, if it exists.

Q.

Obtain the inverse of the following matrix using elementary operations $A=\left[\begin{array}{ccc}0& 1& 2\\ 1& 2& 3\\ 3& 1& 1\end{array}\right]$

Q.

Using elementary transformations, Find the inverse of matrix $\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$ if it exists.

Q. Using elementary row transformations, find the inverse of the matrix $A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 5& 7\\ -2& -4& -5\end{array}\right]$

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}2& -3\\ -1& 2\end{array}\right]$, if it exists.

Q.

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{cc}6& -3\\ -2& 1\end{array}\right]$, if it exists.

Q. Find the number of ways in which 5 boys and 5 girls may be seated in a row so that no two girls and no two boys are together.

Q.

Using elementary transformations, find the inverse of matrix$\left[\begin{array}{cccc}1& 3& -2& \\ -3& 0& -5& \\ 2& 5& 0& \end{array}\right]$, if it exists.

Q.

How is row and column operations are done

Q. $A=\left[\begin{array}{ccc}1& 5& 2\\ 3& 1& 4\\ 2& 2& 3\end{array}\right]$
The following elementary transformations are applied on the matrix A in the given order. The resultant matrix after the following operations $R_2$ $\to$ $R_2$ – $R_3$, $R_1$ $\to$ $R_1–R_2$, $R_3$ $\to$ $R_3$ – 2$R_2$ is

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

Q. If $I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],B=\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$ and $C=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$, then $C=$

1. $I\cos \theta +B\sin \theta$
2. $I\sin \theta +B\cos \theta$
3. $I\cos \theta -B\sin \theta$
4. $-I\cos \theta +B\sin \theta$

Q. Let $\Delta \left(x\right)=\left|\begin{array}{ccc}x+a& x+b& x+a-c\\ x+b& x+c& x-1\\ x+c& x+d& x-b+d\end{array}\right|$ and ${\int }_0^2\Delta \left(x\right)dx=-16$ where a, b, c, d are in A.P.,

1. $\pm$ 1
2. $\pm$ 2
3. $\pm$ 3
4. $\pm$ 4