Question

Solution of the system of Linear equations x+y+2z=9
2x+4y-3z=1
3x+6y-5z-0 is ________________. hu​

Answer 1

Answer:

0 is the answer Please mark me as brainiest

Step-by-step explanation:

Your ‘third equation’ has a typo - I am working on the assumption that it should say ‘3x-6y-5z=0’.

As Gaussian elimination deals with matrices, it is redundant to refer to to matrices in the question.

A better way of asking the question is , perhaps: Using Gaussian elimination, find the values for x, y & z that satisfy the following simultaneous equations: x+y+2z=9, 2x+4y-3z=1 and 3x-6y-5z=0.

Step 1: Set up the matrix

⎡⎣⎢12314−62−3−5⎤⎦⎥⎡⎣⎢xyz⎤⎦⎥=⎡⎣⎢910⎤⎦⎥

Now there is no set order in how to proceed with Gaussian elimination, so my workings below should be seen as just one way to proceed. (It may well be that some other ways are quicker).

Step2: Multiply each row such that the first column only contains ‘6’s

⎡⎣⎢666612−1212−9−10⎤⎦⎥⎡⎣⎢xyz⎤⎦⎥=⎡⎣⎢5430⎤⎦⎥

Step 3: Subtract the first row from the second and third rows

⎡⎣⎢60066−1812−21−22⎤⎦⎥⎡⎣⎢xyz⎤⎦⎥=⎡⎣⎢54−51−54⎤⎦⎥

Step 4: Multiply the second row by 3

⎡⎣⎢600618−1812−63−22⎤⎦⎥⎡⎣⎢xyz⎤⎦⎥=⎡⎣⎢54−153−54⎤⎦⎥

Step 5: Add the second row to the third

⎡⎣⎢600618012−63−85⎤⎦⎥⎡⎣⎢xyz⎤⎦⎥=⎡⎣⎢54−153−207⎤⎦⎥

You can conduct further simplification, but it is not needed as you are now in a position to sol