(Solved): Express the vector \( t \) as a linear combination of the vectors \( u, v \), and \( w \). \[ \math ...

Express the vector \( t \) as a linear combination of the vectors \( u, v \), and \( w \). \[ \mathbf{t}=\left[\begin{array}{r} 1 \\ -12 \\ 17 \end{array}\right], \mathbf{u}=\left[\begin{array}{r} 1 \\ -3 \\ 4 \end{array}\right], \mathbf{v}=\left[\begin{array}{l} 4 \\ 0 \\ 3 \end{array}\right], \mathbf{w}=\left[\begin{array}{r} 1 \\ -2 \\ 4 \end{array}\right] \] \( t=(\quad u+1 \quad v v+1 \quad \mid w \) (Simplify your answer. Use integers or fractions for any numbers in the equation.) Express the vector \( \mathbf{t} \) as a linear combination of the vectors \( \mathbf{u}, \mathbf{v} \), and \( \mathbf{w} \). \[ \mathbf{t}=\left[\begin{array}{r} 0 \\ 0 \\ 17 \end{array}\right], \mathbf{u}=\left[\begin{array}{l} 1 \\ 5 \\ 3 \end{array}\right], \mathbf{v}=\left[\begin{array}{r} -2 \\ -8 \\ 2 \end{array}\right], \mathbf{w}=\left[\begin{array}{r} 3 \\ 5 \\ -14 \end{array}\right] \] \( t=1 \quad \mid u+1 \quad \mathbf{v}+1 \quad \mathbf{w} \) (Simplify your answer. Use integers or fractions for any numbers in the equation.)