Multiply the Matrices [[-1,0],[0,-1]]*[[0,1,1,0],[0,0,1,1]]

Problem

[[−1,0],[0,−1]]*[[0,1,1,0],[0,0,1,1]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 2×2 and the second matrix is 2×4 The resulting matrix will be 2×4

2. Calculate the elements of the first row by multiplying the first row of the left matrix by each column of the right matrix.

(c_11)=(−1)*(0)+(0)*(0)=0

(c_12)=(−1)*(1)+(0)*(0)=−1

(c_13)=(−1)*(1)+(0)*(1)=−1

(c_14)=(−1)*(0)+(0)*(1)=0

3. Calculate the elements of the second row by multiplying the second row of the left matrix by each column of the right matrix.

(c_21)=(0)*(0)+(−1)*(0)=0

(c_22)=(0)*(1)+(−1)*(0)=0

(c_23)=(0)*(1)+(−1)*(1)=−1

(c_24)=(0)*(0)+(−1)*(1)=−1

4. Assemble the resulting matrix using the calculated values.

Final Answer

[[−1,0],[0,−1]]*[[0,1,1,0],[0,0,1,1]]=[[0,−1,−1,0],[0,0,−1,−1]]

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