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Let u = (1,0, -1) and v = (0,2, -1). Determine, if it exists, the value of k so that the vector w = (k, k, -6)

** Function of several variables ** Let u = (1,0, -1) and v = (0,2, -1). Determine, if it exists, the value of k so that the vector w = (k, k, -6) can be expressed as a linear combination of u and v.

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1 %%% 0 %%% -1 0 %%% 2 %%% -1k %%% k %%% -6; If it exists, we must achieve k for the determinant to be 0. -12 - (-k -2k) = 0; -12 +3k = 0; k = 4; Corroboro: -12 - (-4-8) = 0; -12 +12 = 0; it is right.

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