Write as a Vector Equality x-4y=-8 , -x+4y-8=0

Problem

x−4*y=−8,−x+4*y−8=0

Solution

1. Standardize the equations by moving all constant terms to the right side of the equals sign.

x−4*y=−8

−x+4*y=8

2. Identify the coefficients of the variables x and y to form the coefficient matrix.

([1,−4],[−1,4])

3. Define the variable vector and the constant vector.

x=([x],[y])

b=([−8],[8])

4. Construct the vector equality by multiplying the coefficient matrix by the variable vector and setting it equal to the constant vector.

([1,−4],[−1,4])*([x],[y])=([−8],[8])

5. Express as a linear combination of vectors to show the vector equality in terms of the columns of the matrix.

x*([1],[−1])+y*([−4],[4])=([−8],[8])

Final Answer

x*([1],[−1])+y*([−4],[4])=([−8],[8])

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