Mathematics Crash Course BITSAT>Chapter 17 - Matrices and Determinants>Exercise 1>Q 107

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The equations $(λ - 1) x + (3 λ + 1) y + 2 λ z = 0$ , $(λ - 1) x + (4 λ - 2) y + (λ + 3) z = 0$ and $2 x + (3 λ + 1) y + 3 (λ - 1) z = 0$ gives non-trivial solution for some values of $λ$ . Then the ratio $x : y : z$ when $λ$ has the smallest of these values, is

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Important Questions on Matrices and Determinants

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Mathematics Crash Course BITSAT>Chapter 17 - Matrices and Determinants>Exercise 1>Q 108

Consider the system of equations in

x, y

and

z

as

x \sin 3 θ - y + z = 0, x \cos 2 θ + 4 y + 3 z = 0

and

2 x + 7 y + 7 z = 0 .

If this system has a non-trivial solution, then for integer

n,

values of

θ

are given by

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Mathematics Crash Course BITSAT>Chapter 17 - Matrices and Determinants>Exercise 1>Q 109

The following system of linear equations

2 x + 3 y + 2 z = 9

3 x + 2 y + 2 z = 9

x - y + 4 z = 8

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Mathematics Crash Course BITSAT>Chapter 17 - Matrices and Determinants>Exercise 1>Q 110

The system of equations $a x - y - z = a - 1$ , $x - a y - z = a - 1$ , $x - y - a z = a - 1$ has no solution if $' a'$ is

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Mathematics Crash Course BITSAT>Chapter 17 - Matrices and Determinants>Exercise 1>Q 111

The system of linear equations

k x + y + z = 1

,

x + k y + z = 1

and

x + y + k z = 1

has a unique solution under which one of the following conditions?

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Mathematics Crash Course BITSAT>Chapter 17 - Matrices and Determinants>Exercise 1>Q 112

The system of equations $2 x + y - 3 z = 5$ , $3 x - 2 y + 2 z = 5$ and $5 x - 3 y - z = 16$

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Mathematics Crash Course BITSAT>Chapter 17 - Matrices and Determinants>Exercise 1>Q 113

If

[\begin{matrix} 1 & 2 & - 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{matrix}] [\begin{array}{l} x \\ y \\ z \end{array}] = [\begin{array}{l} 1 \\ 1 \\ 1 \end{array}],

then

(x, y, z)

is equal to

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Mathematics Crash Course BITSAT>Chapter 17 - Matrices and Determinants>Exercise 1>Q 114

If

[\begin{array}{l} 1 & 2 & 3 \\ 2 & 4 & 1 \\ 3 & 2 & 9 \end{array}] [\begin{array}{l} x \\ y \\ z \end{array}] = [\begin{matrix} 6 \\ 7 \\ 14 \end{matrix}],

then the values of

x, y, z

respectively are

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Mathematics Crash Course BITSAT>Chapter 17 - Matrices and Determinants>Exercise 1>Q 115

The system of linear equations

(λ + 3) x + (λ + 2) y + z = 0

,

3 x + (λ + 3) y + z = 0

and

2 x + 3 y + z = 0

has non-trivial solutions,