The vectors mathbf a =(1,2,3), mathbf b =(2,5,7), mathbf c =(1,3,5) — to test linear (in)dependence, we compute detbegin pmatrix 1&2&32&5&71&3&5end pmatrix . The value of this determinant is:

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SSC Pure Mathematics QUESTION #4089

Question 1

The vectors \(\mathbf{a}=(1,2,3)\), \(\mathbf{b}=(2,5,7)\), \(\mathbf{c}=(1,3,5)\) — to test linear (in)dependence, we compute \(\det\begin{pmatrix}1&2&3\\2&5&7\\1&3&5\end{pmatrix}\). The value of this determinant is:

\(0\)
\(1\)✔️
\(-1\)
\(2\)

Correct Answer Explanation

Expanding along row 1: \(1(5\cdot5-7\cdot3)-2(2\cdot5-7\cdot1)+3(2\cdot3-5\cdot1) = 1(25-21)-2(10-7)+3(6-5) = 4-6+3=1\). Since det \(=1\neq 0\), the vectors are linearly INDEPENDENT.

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