Determine if Linear [[4,-3],[3,1]][[x],[y]]=[[-3],[4]]

Problem

[[4,−3],[3,1]]*[[x],[y]]=[[−3],[4]]

Solution

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

2. Recall the definition of a linear system, where each equation must be a linear combination of the variables x and y equal to a constant.

3. Expand the matrix multiplication to see the individual equations.

4. Perform the multiplication of the first row by the column vector.

4*x−3*y=−3

5. Perform the multiplication of the second row by the column vector.

3*x+1*y=4

6. Observe that both equations are in the form a*x+b*y=c where a b and c are constants.

7. Conclude that because the variables are only raised to the first power and are not multiplied together or used in non-linear functions, the system is linear.

Final Answer

[[4,−3],[3,1]]*[[x],[y]]=[[−3],[4]]⇒Linear

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