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3 years ago

What is the solution to the matrix equation [2 1 1 0]x=5/10

Mathematics

1 answer:

Mama L [17]3 years ago

6 0

[2 1 | 1 0 ] • x = [5 | 10]

We multiply by the inverse of

[2 1 | 1 0 ]

det( [2 1 | 1 0] ) = -1

=> [2 1 | 1 0 ]^(-1) = (-1)•[0 -1 | -1 2 ] =

= [0 1 | 1 -2]

=> [2 1 | 1 0 ] • x = [5 | 10]

=> x = [2 1 | 1 0 ]^(-1) • [5 | 10]

=> x = [0 1 | 1 -2] • [5 | 10]

=> x = [0+10 | 5-20]

=> x = [10 | -15]

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4 years ago

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dangina [55]

For this case we have the following equation:

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Subtracting $\frac {1} {6} g$ to both sides of the equation:

$\frac {5} {9} g- \frac {1} {6} + 10 = 3\\\frac {6 * 5-9 * 1} {9 * 6} g + 10 = 3\\\frac {30-9} {54} g + 10 = 3\\\frac {21} {54} g + 10 = 3\\\frac {7} {18} g + 10 = 3$