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Given that m=(2,-7) and n=(5,1) solve the following vector equation @ xm-yn=(9,13)?

Mar 11

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Mar 11

To solve the vector equation xm - yn = (9,13), we need to find the values of x and y that satisfy the equation.

Given that m = (2,-7) and n = (5,1), we can substitute these values into the equation:

x(2,-7) - y(5,1) = (9,13)

Expanding the equation, we get:

(2x, -7x) - (5y, y) = (9,13)

Now, we can separate the equation into two separate equations for the x and y components:

2x - 5y = 9

-7x - y = 13

Now, we can solve this system of equations to find the values of x and y:

From the first equation:

2x - 5y = 9

2x = 5y + 9

x = (5y + 9)/2

Substitute x into the second equation:

-7((5y + 9)/2) - y = 13

-35y/2 - 63/2 - y = 13

-35y - 63 - 2y = 26

-37y = 89

y = -89/37

Now, substitute y back into the equation for x:

x = (5(-89/37) + 9)/2

x = (-445/37 + 333/37)/2

x = -112/37

Therefore, the solution to the vector equation xm - yn = (9,13) is x = -112/37 and y = -89/37.

Given that m = (2,-7) and n = (5,1), we can substitute these values into the equation:

x(2,-7) - y(5,1) = (9,13)

Expanding the equation, we get:

(2x, -7x) - (5y, y) = (9,13)

Now, we can separate the equation into two separate equations for the x and y components:

2x - 5y = 9

-7x - y = 13

Now, we can solve this system of equations to find the values of x and y:

From the first equation:

2x - 5y = 9

2x = 5y + 9

x = (5y + 9)/2

Substitute x into the second equation:

-7((5y + 9)/2) - y = 13

-35y/2 - 63/2 - y = 13

-35y - 63 - 2y = 26

-37y = 89

y = -89/37

Now, substitute y back into the equation for x:

x = (5(-89/37) + 9)/2

x = (-445/37 + 333/37)/2

x = -112/37

Therefore, the solution to the vector equation xm - yn = (9,13) is x = -112/37 and y = -89/37.