Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 45

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IMPORTANT

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In a third order of determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then, it can be decomposed into $n$ determinants, where $n$ has value

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Important Questions on Determinant

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 46

If

p q r \neq 0

and the system of equations

$(p + a) x + b y + c z = 0$

$a x + (q + b) y + c z = 0$

$a x + b y + (r + c) z = 0$

has a non-trivial solution, then value of $\frac{a}{p} + \frac{b}{q} + \frac{c}{r}$ is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 47

The number of solutions of

2 x + y = 4, x - 2 y = 2, 3 x + 5 y = 6

is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 49

The value of

a

for which the system of equations

$a^{3} x + {(a + 1)}^{3} y + {(a + 2)}^{3} z = 0$

$a x + (a + 1) y + (a + 2) z = 0$

$x + y + z = 0$

has a non-zero solution, is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 50

If

C = 2 \cos θ,

then the value of the determinant

Δ = |\begin{array}{l} C & 1 & 0 \\ 1 & C & 1 \\ 0 & 1 & C \end{array}|

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 51

Consider the system of equations

a_{1} x + b_{1} y + c_{1} z = 0, a_{2} x + b_{2} y + c_{2} z = 0, a_{3} x + b_{3} y + c_{3} z = 0 .

If

|\begin{array}{l} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{array}| = 0,

then the system has

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 52

If

a > b > c

and the system of equations

a x + b y + c z = 0

,

b x + c y + a z = 0

and

c x + a y + b z = 0

has a non-trivial solution, then both the roots of the quadratic equation

a t^{2} + b t + c = 0

are

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 53

The multiplicative inverse of

A = [\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}]

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 54

If

a, b

and

c

are non-zero real numbers, then the inverse of the matrix

A = [\begin{array}{l} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{array}]

is