Question

If $a_{ij}=\begin{cases} 0,& i\ne j\\ 2i-j,& i=j \end{cases}$ then matrix A is:

• A. diagonal matrix type 1
• B. diagonal matrix type 2
• C. diagonal matrix type 3
• D. diagonal matrix type 4

Hint:

Diagonal matrix means all non-diagonal entries are zero, regardless of formula complexity.

Answer 1

The Correct Option is A, D

Concept: A matrix is diagonal if all off-diagonal elements are zero.

Step 1: {Check off-diagonal entries.}
\[ a_{ij}=0 \quad (i\ne j) \]

Step 2: {Compute diagonal entries.}
\[ a_{ii}=2i-i=i \]

Step 3: {Write full matrix.}
\[ A= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix} \]

Step 4: {Hence matrix is diagonal with increasing diagonal values.}

Step 5: {Correct statements correspond to diagonal matrix properties (A and D).}