Question

A diogonal matrix is said to be a........ if its diagonal elements are equal ( other than unity) I. fill the blank

Answer 1

I think it may Identity matrix
example for identity matrix is    

  

      2      0                                4   0   0

      0      2                                0    4  0

                                                0    0   4  

Answer 2

A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal ( other than unity)

Given :

A diagonal matrix is said to be a _____ if its diagonal elements are equal ( other than unity)

To find :

To fill in the blank

Solution :

Step 1 of 2 :

Define diagonal matrix

A square matrix is said to be a diagonal matrix if the elements other than the diagonal elements are zero

The diagonal matrix $\sf{(d_{ij})_{n,n }}$

$\sf{is \: denoted \: by \: \: diag(d_{11},d_{12}, ....,d_{nn})}$

For example the below matrix is a diagonal matrix

$\displaystyle\begin{pmatrix} 4 & 0 & 0\\ 0 & 2 & 0 \\ 0 & 0 & 1 \end{pmatrix}$

Step 2 of 2 :

Find the required matrix

We know a diagonal matrix is said to be a scalar matrix if its diagonal elements are equal ( other than unity)

For example the below matrix is a scalar matrix

$\displaystyle\begin{pmatrix} 2 & 0 & 0\\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{pmatrix}$

Hence we can conclude that a diagonal matrix is said to be a scalar matrix if its diagonal elements are equal ( other than unity)

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