Find the Inverse of the Resulting Matrix [[1,0,4],[0,1,3],[0,0,0]]*[[4],[2],[0]]

Problem

[[1,0,4],[0,1,3],[0,0,0]]*[[4],[2],[0]]

Solution

1. Multiply the 3×3 matrix by the 3×1 column vector using the dot product of each row with the vector.

(R_1)=(1)*(4)+(0)*(2)+(4)*(0)=4

(R_2)=(0)*(4)+(1)*(2)+(3)*(0)=2

(R_3)=(0)*(4)+(0)*(2)+(0)*(0)=0

2. Identify the resulting matrix from the multiplication.

[[4],[2],[0]]

3. Determine if the resulting matrix has an inverse. An inverse only exists for square matrices (n×n that are non-singular (determinant is non-zero).

4. Conclude that since the resulting matrix is a 3×1 column vector and not a square matrix, it cannot have an inverse.

Final Answer

The resulting matrix *[[4],[2],[0]]* is not square and has no inverse.

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