Math  /  Algebra

QuestionIs the vector u=[7108]u=\begin{bmatrix}-7 \\ 10 \\ 8\end{bmatrix} in the plane spanned by the columns of A=[245722]A=\begin{bmatrix}2 & -4 \\ -5 & 7 \\ 2 & 2\end{bmatrix}? Explain.

Studdy Solution
The last row of the reduced row-echelon form of the matrix is inconsistent ( =42), so the system of equations has no solution. Therefore, the vector uu is not in the plane spanned by the columns of AA.
The correct choice is A. The reduced echelon form of the augmented matrix is [7/5215/242]\left[\begin{array}{rr|r} & -7/5 & -2 \\ & & -15/2 \\ & &42\end{array}\right], which is an inconsistent system.

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