Question

If A = diag (1,-1, 2), B = diag (2, 3,-1) then 3A +4B​

Answer 1

SOLUTION

GIVEN

• A = diag (1,-1, 2)

• B = diag (2, 3,-1)

TO DETERMINE

3A +4B

CONCEPT TO BE IMPLEMENTED

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

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

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

EVALUATION

Here it is given that

A = diag (1,-1, 2)

B = diag (2, 3,-1)

$A = \displaystyle\begin{vmatrix} 1 & 0 & 0\\ 0 & - 1 & 0 \\ 0 & 0 & 2 \end{vmatrix}$

$B = \displaystyle\begin{vmatrix} 2 & 0 & 0\\ 0 & 3 & 0 \\ 0 & 0 & - 1 \end{vmatrix}$

$\therefore \: 3A = \displaystyle\begin{vmatrix} 3 & 0 & 0\\ 0 & - 3 & 0 \\ 0 & 0 & 6 \end{vmatrix}$

$\therefore \: 4B = \displaystyle\begin{vmatrix} 8 & 0 & 0\\ 0 & 12 & 0 \\ 0 & 0 & - 4 \end{vmatrix}$

Hence 3A + 4B

$= \displaystyle\begin{vmatrix} 3 & 0 & 0\\ 0 & - 3 & 0 \\ 0 & 0 & 6 \end{vmatrix} + \displaystyle\begin{vmatrix} 8 & 0 & 0\\ 0 & 12 & 0 \\ 0 & 0 & - 4 \end{vmatrix}$

$= \displaystyle\begin{vmatrix} 11 & 0 & 0\\ 0 & 9 & 0 \\ 0 & 0 & 2 \end{vmatrix}$

= diag (11 , 9 , 2)

FINAL ANSWER

3A + 4B = = diag (11 , 9 , 2)

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