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Mathematics Question on Transpose of a Matrix

Find the scalars λ1 and λ2 that are attached to v=[1 2 ]v=\begin{bmatrix} 1\\\ 2 \\\ \end{bmatrix} and w=[3 1 ]w=\begin{bmatrix} 3\\\ 1 \\\ \end{bmatrix} to yield[1 0 ]\begin{bmatrix} 1\\\ 0 \\\ \end{bmatrix}

A

λ1=25,λ2=−25λ_1=\frac{2}{5}, λ_2=-\frac{2}{5}

B

λ1=−15,λ2=25λ_1=-\frac{1}{5}, λ_2=\frac{2}{5}

C

λ1=5,λ2=15λ_1=5, λ_2=\frac{1}{5}

D

λ1=−15,λ2=−25λ_1=-\frac{1}{5}, λ_2=-\frac{2}{5}

Answer

λ1=−15,λ2=25λ_1=-\frac{1}{5}, λ_2=\frac{2}{5}

Explanation

Solution

The correct option is(B): λ1=−15,λ2=25λ_1=-\frac{1}{5}, λ_2=\frac{2}{5}