If $v_{1}=(1,0,3) ; v_{2}=(0,2,4) ; v_{3}=(3, x, 1)$ are linearly dependent vectors in $R^{3}$ find the value for $x$ ?
(A) 6
(B) 1
(C) 5
(D) 0
(E) -4

Answer

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Answer

Solve for x: $\boxed{-4}$

Steps

Step 1 ：Since the vectors are linearly dependent, the determinant of the matrix formed by these vectors should be equal to 0. Calculate the determinant: $\begin{vmatrix} 1 & 0 & 3 \\ 0 & 2 & x \\ 3 & 4 & 1 \end{vmatrix}$

Step 2 ：Solve for x: $\boxed{-4}$

If $v_{1}=(1,0,3) ; v_{2}=(0,2,4) ; v_{3}=(3, x, 1)$ are linearly dependent vectors in $R^{3}$ find the value for $x$ ?(A) 6(B) 1(C) 5(D) 0(E) -4

Answer

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If $v_{1}=(1,0,3) ; v_{2}=(0,2,4) ; v_{3}=(3, x, 1)$ are linearly dependent vectors in $R^{3}$ find the value for $x$ ?
(A) 6
(B) 1
(C) 5
(D) 0
(E) -4