Which of the following is a diagonal matrix?

Mathematics

2 answers:

IRINA_888 [86]3 years ago

5 0

A matrix is diagonal if

$i\neq j \implies A_{i,j}=0$

In other words, you want non-zero elements only when the indices of the row and the column are the same: the first element of the first row must be non zero, the second element of the second row must be non-zero, and so on. All other elements must be zero.

xxTIMURxx [149]3 years ago

5 0

Answer:

Option 3

Step-by-step explanation:

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2) ELIMINATION
I'll show you both:

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y = - 3x + 208
plug what y is equal to in 1st equation into the y of the 2nd:
2x + 160 = -3x + 208
2x + 3x + 160 = -3x + 3x + 208
5x + 160 -160 = 208 - 160
5x = 48
5x/5 = 48/5
x = 48/5 = 9 3/5
now plug that x into either one of the original equations: y = -3x + 208 = -3(48/5) + 208
y = -144/5 + 208 = 1040/5 - 144/5 = 896/5
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2) add the whole equations together so as to cancel out one of the variables:
I'm choosing to eliminate the y, so we need y-y to remove the y's, I'll multiply the whole 2nd equation by -1 to make that -y
-1 (y = - 3x + 208)
-y = 3x - 208
So set it up like:
y = 2x + 160
-[y = 3x - 208]
---------------------
0 = 5x - 48
0+48 = 5x -48 +48
5x = 48
5x/5 = 48/5
x = 48/5
plug that x value into one of the original equations: y = 2x + 160 = 2(48/5) + 160
y = 96/5 + 160 = 96/5 + 800/5 = 896/5
y = 179 1/5

SO WE GOT THE SAME VALUES BOTH WAYS.
WHEN YOU SEE FUTURE PROBLEMS LIKE THESE, SOME WILL BE QUICKER BY ELIMINATION AND OTHERS BY SUBSTITUTION

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