Add 3a+4a*[[2,2],[3,-3]]

Problem

3*a+4*a*[[2,2],[3,−3]]

Solution

1. Identify the scalar multiplication required for the matrix term.

2. Multiply each element of the matrix by the scalar 4*a

4*a*[[2,2],[3,−3]]=[[4*a(2),4*a(2)],[4*a(3),4*a*(−3)]]

3. Simplify the resulting matrix elements.

[[8*a,8*a],[12*a,−12*a]]

4. Add the scalar 3*a to the matrix. In matrix algebra, adding a scalar k to a matrix M is typically interpreted as M+k*I where I is the identity matrix of the same dimension.

3*a*[[1,0],[0,1]]+[[8*a,8*a],[12*a,−12*a]]

5. Perform the matrix addition by adding corresponding elements.

[[3*a+8*a,0+8*a],[0+12*a,3*a−12*a]]

6. Combine like terms to find the final matrix.

[[11*a,8*a],[12*a,−9*a]]

Final Answer

3*a+4*a*[[2,2],[3,−3]]=[[11*a,8*a],[12*a,−9*a]]

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