Diagonal Matrix

Q. All the non diagonal elements of a diagonal matrix are ______.

1. 2
2. 0
3. 1
4. non-zero

Q.

A square matrix in which all the entries above the leading diagonal are zero is called a _________.

1. Row Matrix

2. Upper triangular matrix

3. Diagonal Matrix

4. Lower triangular matrix

Q.

A diagonal matrix will always be

1. Rectangular matrix

2. Identity matrix

3. Square matrix

4. None of these

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 $i=j$

1. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 4& 0\\ 0& 0& 9\end{array}\right]$

2. $\left[\begin{array}{ccc}1& 1& 1\\ 4& 4& 4\\ 9& 9& 9\end{array}\right]$

3. $\left[\begin{array}{ccc}0& 1& 1\\ 4& 0& 4\\ 9& 9& 0\end{array}\right]$

4. $\left[\begin{array}{ccc}-1& 0& 0\\ 0& -4& 0\\ 0& 0& -9\end{array}\right]$

Q. Match the type of matrices with their corresponding ​examples:
​

Q.

Consider two matrices A and B. $(A+B{)}^T$ = __________

1. (AB)^T

2. AB

3. A^T + B^T

4. BA

Q.

$A=\left[\begin{array}{ccc}1& 0& 0\\ 0& -5& 0\\ 0& 0& 9\end{array}\right]$ is a ________.

1. rectangular matrix

2. diagonal matrix

3. scalar matrix

4. unit matrix

Q.

Given $A=\left[\begin{array}{ccc}2& -6& 0\\ -1& 5& 8\\ 3& -2& 4\end{array}\right]\text{and}C=\left[\begin{array}{ccc}3& 0& 0\\ 0& 2& 0\\ 0& 0& 1\end{array}\right]$

Find a matrix B, such that A+B=C

1. $\left[\begin{array}{ccc}1& 6& 0\\ 1& 3& 8\\ 3& 2& 3\end{array}\right]$

2. $\left[\begin{array}{ccc}1& 6& 0\\ 1& -3& 8\\ -3& 0& 3\end{array}\right]$

3. $\left[\begin{array}{ccc}1& 6& 0\\ 1& -3& -8\\ -3& 2& -3\end{array}\right]$

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

Q.

Which one of the following statements is not true?

1. A diagonal matrix is a square matrix.

2. A scalar matrix is a square matrix.

3. A scalar matrix is a diagonal matrix.

4. A diagonal matrix is a scalar matrix.

Q. $\underset{x\to 1}{lim}(1-x)\tan \left(\begin{array}{c}\frac{\pi x}{2}\end{array}\right)$ is equal to -

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

Q.

A main diagonal is a set of all elements which satisfy the condition i $\ne$ j.

1. True

2. False