Subtract the Matrices

Problem

x*[[1,0,0],[0,1,0],[0,0,1]]−[[−1,0,1],[−2,0,−1],[0,0,1]]

Solution

1. Perform scalar multiplication by multiplying every element in the first matrix by x

x*[[1,0,0],[0,1,0],[0,0,1]]=[[x,0,0],[0,x,0],[0,0,x]]

2. Set up the subtraction by placing the two matrices in a single expression.

[[x,0,0],[0,x,0],[0,0,x]]−[[−1,0,1],[−2,0,−1],[0,0,1]]

3. Subtract corresponding elements from each position in the matrices.

[[x−(−1),0−0,0−1],[0−(−2),x−0,0−(−1)],[0−0,0−0,x−1]]

4. Simplify the entries by performing the basic arithmetic operations.

[[x+1,0,−1],[2,x,1],[0,0,x−1]]

Final Answer

x*[[1,0,0],[0,1,0],[0,0,1]]−[[−1,0,1],[−2,0,−1],[0,0,1]]=[[x+1,0,−1],[2,x,1],[0,0,x−1]]

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