Question

if A= diag (4,2,1) then det A is equal to​

Answer 1

Answer:

8

Step-by-step explanation:

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Answer 2

SOLUTION

GIVEN

A= diag (4,2,1)

TO DETERMINE

det A

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 (4,2,1)

$\therefore \: \:A = \displaystyle\begin{pmatrix} 4 & 0 & 0\\ 0 & 2 & 0 \\ 0 & 0 & 1 \end{pmatrix}$

$\therefore \: \:det \: A = \displaystyle\begin{vmatrix} 4 & 0 & 0\\ 0 & 2 & 0 \\ 0 & 0 & 1 \end{vmatrix}$

$\implies \: \:det \: A = 4(2 \times 1 - 0) + 0 + 0$

$\implies \: \:det \: A = 8$

FINAL ANSWER

If A= diag (4,2,1) then det A = 8

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