If $A = diag (4, 5, 9)$ and $B = diag (- 1, - 2, - 4)$ , then $2 A + 4 B$ is:

diag (17, 0, - 2)

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2 diag (2, 1, 1)

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diag (2, 1, 1)

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diag (0, - 7, 17)

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Solution

The correct option is B $2 diag (2, 1, 1)$
Given : $A = diag (4, 5, 9)$
and $B = diag (- 1, - 2, - 4)$ ,
Now, $2 A + 4 B$
$= 2 diag (4, 5, 9) + 4 diag (- 1, - 2, - 4)$
$= diag (8, 10, 18) + diag (- 4, - 8, - 16)$
$= diag (8 - 4, 10 - 8, 18 - 16)$
$= diag (4, 2, 2)$
Hence, $2 A + 4 B = 2 diag (2, 1, 1)$

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