Consider vectors $\mathbf{a} = (1, 2, 3)$, $\mathbf{b} = (2, 5, 7)$, $\mathbf{c} = (1, 3, 5)$ in $\mathbb{R}^3$. Compute $\det \begin{pmatrix} 1 & 2 & 1 \ 2 & 5 & 3 \ 3 & 7 & 5 \end{pmatrix}$. What does this indicate?

Home › MCQs › CSS Pure Mathematics › Question #4115

CSS Pure Mathematics QUESTION #4115

Question 1

Determinant is $0$, vectors are linearly dependent
Determinant is $1$, vectors are linearly independent✔️
Determinant is $-1$, vectors are linearly independent
Determinant is $2$, vectors are linearly dependent

Correct Answer Explanation

$\det = 1(25-21) - 2(10-9) + 1(14-15) = 4 - 2 - 1 = 1 \neq 0$. Since determinant is non-zero, the vectors are linearly independent.

More Options