Determine if Linear

Problem

[[5,−3,12],[2,3,9]]*[[x],[y],[z]]=[[26],[2]]

Solution

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

2. Analyze the components of the equation, where A is a matrix of constants, x is a vector of variables, and b is a vector of constants.

3. Expand the matrix multiplication into a system of equations to check the degree of the variables.

4. Observe that the resulting equations are 5*x−3*y+12*z=26 and 2*x+3*y+9*z=2

5. Conclude that since all variables x y and z appear only to the first power and are not multiplied by each other, the system is linear.

Final Answer

The system is linear.

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