From the following matrices identify diagonal, scalar and unit (identity) matrices.

Question

Question:

From the following matrices identify diagonal, scalar and unit (identity) matrices.

A =$~\left[ \begin{matrix} 4 & 0 \ 0 & 4 \ \end{matrix} ight]$	B =$~\left[ \begin{matrix} 2 & 0 \ 0 & -1 \ \end{matrix} ight]$
C =$\left[ \begin{matrix} 1 & 0 \ 0 & 1 \ \end{matrix} ight]$	D = $\left[ \begin{matrix} 3 & 0 \ 0 & 0 \ \end{matrix} ight]$
E =$\left[ \begin{matrix} 5-3 & 0 \ 0 & 1+1 \ \end{matrix} ight]$

Accepted Answer

Solution:

Matrix A is a scalar matrix (because its diagonal entries are same).

Matrix B is a diagonal matrix (because its diagonal entries are non-zero and non-diagonal entities are zero).

Matrix C is an identity matrix (because its diagonal entries are $1$).

Matrix D is a diagonal matrix (because its one diagonal entry is non-zero and non-diagonal entities are zero).

Matrix E is a scalar matrix (because its diagonal entries are same).

E = $\left[ \begin{matrix} 5-3 & 0 \ 0 & 1+1 \ \end{matrix} ight]$

E = $\left[ \begin{matrix} 2 & 0 \ 0 & 2 \ \end{matrix} ight]$

Note:

All the matrices A, B, C, D and E are diagonal matrices because they have at least one non-zero diagonal entry and all their non-diagonal entries are zero. Scalar and unit matrices are further types of diagonal matrices.

A =$~\left[ \begin{matrix} 4 & 0 \\ 0 & 4 \\ \end{matrix} \right]$	B =$~\left[ \begin{matrix} 2 & 0 \\ 0 & -1 \\ \end{matrix} \right]$
C =$\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]$	D = $\left[ \begin{matrix} 3 & 0 \\ 0 & 0 \\ \end{matrix} \right]$
E =$\left[ \begin{matrix} 5-3 & 0 \\ 0 & 1+1 \\ \end{matrix} \right]$