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

Problem

(([1],[2],[0])*([0,2,1]))(−1)

Solution

1. Multiply the given matrices to find the resulting matrix A Since we are multiplying a 3×1 matrix by a 1×3 matrix, the result is a 3×3 matrix.

A=([1*(0),1*(2),1*(1)],[2*(0),2*(2),2*(1)],[0*(0),0*(2),0*(1)])

A=([0,2,1],[0,4,2],[0,0,0])

2. Check for invertibility by calculating the determinant of matrix A

det(A)=0*(4⋅0−2⋅0)−2*(0⋅0−2⋅0)+1*(0⋅0−4⋅0)

det(A)=0

3. Conclude that the matrix does not have an inverse. A matrix is invertible if and only if its determinant is non-zero. Since the determinant is 0 (and the matrix has a row and a column of zeros), it is singular.

Final Answer

The matrix *([0,2,1],[0,4,2],[0,0,0])* is singular and has no inverse.

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