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Matrices and Determinants question

2018 · Shift 2 · Q21

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JEE Advanced
Mathematics
Matrices and Determinants
2018 · Shift 2 · Q21

Matrices and Determinants question

2018 · Shift 2 · Q21

JEE AdvancedMathematicsMatrices and DeterminantsMultiple correct+4 / −1

Let S be the set of all column matrices

\left[ {\begin{matrix} {{b_1}} \\ {{b_2}} \\ {{b_3}} \\ \end{matrix} } \right]

such that

{b_1},{b_2},{b_3} \in R

and the system of equations (in real variables)

\begin{aligned} & - x + 2y + 5z = {b_1} \\ & 2x - 4y + 3z = {b_2} \\ & x - 2y + 2z = {b_3} \\\end{aligned}

has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each

\left[ {\begin{matrix} {{b_1}} \\ {{b_2}} \\ {{b_3}} \\ \end{matrix} } \right]

\in

S?

A
$x + 2y + 3z = {b_1}$ , $\,4y + 5z = {b_2}$ and $x + 2y + 6z = {b_3}$
B
$x + y + 3z = {b_1}$ , $5x + 2y + 6z = {b_2}$ and $- 2x - y - 3z = {b_3}$
C
$- x + 2y - 5z = {b_1}$ , $\,2x - 4y + 10z = {b_2}$ and $x - 2y + 5z = {b_3}$
D
$x + 2y + 5z = {b_1}$ , $2x + 3z = {b_2}$ and $x + 4y - 5z = {b_3}$

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