6. If the set left{left[begin{array}{c}4 3 11end{array}right],left[begin{array}{c}-2 0 -4end{array}right],left[begin{array}{l}3 a 5end{array}right]right} in mathbb{R}^{3} is linearly independent, what value can a not be?

Question

6. If the set left{left[begin{array}{c}4  3  11end{array}right],left[begin{array}{c}-2  0  -4end{array}right],left[begin{array}{l}3  a  5end{array}right]right} in mathbb{R}^{3} is linearly independent, what value can a not be?

Accepted Answer

Step:1 ：Form the matrix and calculate its determinant: begin{vmatrix} 4 & -2 & 3  3 & 0 & a  11 & -4 & 5 end{vmatrix} = -6a - 6Step:2 ：Set the determinant equal to zero and solve for &#x27;a&#x27;: -6a - 6 = 0 Rightarrow a = boxed{-1}

Answer

Step: 1 ：Form the matrix and calculate its determinant: begin{vmatrix} 4 & -2 & 3  3 & 0 & a  11 & -4 & 5 end{vmatrix} = -6a - 6Step: 2 ：Set the determinant equal to zero and solve for &#x27;a&#x27;: -6a - 6 = 0 Rightarrow a = boxed{-1}

6. If the set ${[\begin{matrix} 4 \\ 3 \\ 11 \end{matrix}], [\begin{matrix} - 2 \\ 0 \\ - 4 \end{matrix}], [\begin{array}{l} 3 \\ a \\ 5 \end{array}]}$ in $R^{3}$ is linearly independent, what value can $a$ not be?

Answer

Popular Problems

6. If the set {[4311],[−20−4],[3a5]} in R3 is linearly independent, what value can a not be?

Answer

Popular Problems

6. If the set ${[\begin{matrix} 4 \\ 3 \\ 11 \end{matrix}], [\begin{matrix} - 2 \\ 0 \\ - 4 \end{matrix}], [\begin{array}{l} 3 \\ a \\ 5 \end{array}]}$ in $R^{3}$ is linearly independent, what value can $a$ not be?