Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 42

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IMPORTANT

Earn 100

The system of linear equations
$3 x - 2 y - k z = 10$

$2 x - 4 y - 2 z = 6$

$x + 2 y - z = 5 m$
is inconsistent if :

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Important Questions on Matrices and Determinants

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 43

Let the system of linear equations

4 x + λ y + 2 z = 0

2 x - y + z = 0

μ x + 2 y + 3 z = 0, λ, μ \in R

has a non-trivial solution. Then which of the following is true?

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 44

The system of linear equations

x + y + z = 2

,

3 x - y + 2 z = 6

and

3 x + y + z = - 18

has

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 45

If $(\frac{a_{1}}{x}) + (\frac{b_{1}}{y}) = c_{1}, (\frac{a_{2}}{x}) + (\frac{b_{2}}{y}) = c_{2}$ , $Δ_{1} = |\begin{array}{l} a_{1} & b_{1} \\ a_{2} & b_{2} \end{array}|, Δ_{2} = |\begin{array}{l} b_{1} & c_{1} \\ b_{2} & c_{2} \end{array}|, Δ_{3} = |\begin{array}{l} c_{1} & a_{1} \\ c_{2} & a_{2} \end{array}|$ , then $(x, y)$ is equal to which one of the following?

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 46

If

l + m + n = 0,

then the system of equations

- 2 x + y + z = l, x - 2 y + z = m, x + y - 2 z = n

has

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 47

The system of equations

k x + y + z = 1, x + k y + z = k

and

x + y + k z = k^{2}

has no solution if

k

equals.

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 48

If

3 x - 4 y + 2 z = - 1, 2 x + 3 y + 5 z = 7, x + z = 2

, then

x =

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 49

If

[\begin{array}{r} 1 & 1 & 1 \\ 1 & - 2 & - 2 \\ 1 & 3 & 1 \end{array}] [\begin{array}{l} x \\ y \\ z \end{array}] = [\begin{array}{l} 0 \\ 3 \\ 4 \end{array}],

then

[\begin{array}{l} x \\ y \\ z \end{array}]

is equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 50

If the system of linear equations,

x + 2 a y + a z = 0

,

x + 3 b y + b z = 0

and

x + 4 c y + c z = 0

has a non-zero solution, then

a, b

and

c

satisfy