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: $- 4$

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: $| \begin{matrix} 1 & 0 & 3 \\ 0 & 2 & x \\ 3 & 4 & 1 \end{matrix} |$

Step 2 ：Solve for x: $- 4$

If v1=(1,0,3);v2=(0,2,4);v3=(3,x,1) are linearly dependent vectors in R3 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