Simplify the Matrix 2[[1,8],[2,1]]+4

Problem

2*[[1,8],[2,1]]+4

Solution

1. Interpret the expression as a scalar multiplication of a matrix followed by the addition of a scalar to the resulting matrix. In matrix algebra, adding a scalar k to a matrix A is typically interpreted as A+k*I where I is the identity matrix.

2. Perform scalar multiplication by multiplying every entry in the matrix by 2.

2*[[1,8],[2,1]]=[[2*(1),2*(8)],[2*(2),2*(1)]]

[[2*(1),2*(8)],[2*(2),2*(1)]]=[[2,16],[4,2]]

3. Add the scalar 4 to the matrix by adding 4 to each diagonal entry (treating 4 as 4*I.

[[2,16],[4,2]]+[[4,0],[0,4]]=[[2+4,16+0],[4+0,2+4]]

4. Simplify the resulting entries to find the final matrix.

[[2+4,16+0],[4+0,2+4]]=[[6,16],[4,6]]

Final Answer

2*[[1,8],[2,1]]+4=[[6,16],[4,6]]

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