Find the Inverse of the Resulting Matrix [[-1,3]][[3,4]]

Problem

[[−1,3]]*[[3],[4]]

Solution

1. Multiply the matrices to find the resulting value. Since the first matrix is 1×2 and the second is 2×1 the result is a 1×1 matrix (a scalar).

(−1)*(3)+(3)*(4)

2. Simplify the arithmetic to find the single element of the matrix.

−3+12=9

3. Identify the resulting 1×1 matrix.

[9]

4. Find the inverse of the 1×1 matrix. For a 1×1 matrix [a] the inverse is [a(−1)] or [1/a] provided a≠0

1/9

Final Answer

([[−1,3]]*[[3],[4]])(−1)=[1/9]

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