Determine if Linear [[1,5],[4,8]]*[[x],[y]]=[[-20],[-44]]

Problem

[[1,5],[4,8]]*[[x],[y]]=[[−20],[−44]]

Solution

1. Identify the structure of the given equation, which is in the form A*x=b

2. Expand the matrix multiplication on the left side by multiplying the rows of the first matrix by the column vector of variables.

3. Write the resulting system of equations by setting each component of the resulting vector equal to the corresponding component on the right side.

4. Observe that the first equation is 1*x+5*y=−20

5. Observe that the second equation is 4*x+8*y=−44

6. Conclude that since both equations are of the form a*x+b*y=c where the variables x and y are raised only to the first power and are not multiplied together, the system is linear.

Final Answer

[[1,5],[4,8]]*[[x],[y]]=[[−20],[−44]]⇒Linear

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