Multiply the Matrices 2[[1,0,-3,2],[4,1,-2,5],[2,1,4,1]]

Problem

2*[[1,0,−3,2],[4,1,−2,5],[2,1,4,1]]

Solution

1. Identify the operation as scalar multiplication, where every entry in the matrix is multiplied by the constant 2

2. Multiply each element in the first row by 2

2*(1)=2

2*(0)=0

2*(−3)=−6

2*(2)=4

3. Multiply each element in the second row by 2

2*(4)=8

2*(1)=2

2*(−2)=−4

2*(5)=10

4. Multiply each element in the third row by 2

2*(2)=4

2*(1)=2

2*(4)=8

2*(1)=2

5. Assemble the resulting values into a new matrix of the same dimensions (3×4.

Final Answer

2*[[1,0,−3,2],[4,1,−2,5],[2,1,4,1]]=[[2,0,−6,4],[8,2,−4,10],[4,2,8,2]]

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