HARD

Earn 100

In a third order 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 $n$ determinant, where $n$ has the value

50% studentsanswered this correctly

Important Questions on Matrices and Determinants

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

a_{1}, a_{2}, a_{3}, \dots \dots a_{9}

are in

AP

, then the value of

|\begin{array}{l} a_{1} & a_{2} & a_{3} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9} \end{array}|

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

a + x = b + y = c + z + 1,

where

a, b, c, x, y, z

are non-zero distinct real numbers, then

|\begin{array}{l} x & a + y & x + a \\ y & b + y & y + b \\ z & c + y & z + c \end{array}|

is equal to :

HARD

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

Δ = |\begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 \\ 2 x - 3 & 3 x - 4 & 4 x - 5 \\ 3 x - 5 & 5 x - 8 & 10 x - 17 \end{matrix}| = A x^{3} + B x^{2} + C x + D

, then

B + C

is equal to :

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

a_{r} = (\cos 2 r π + i \sin 2 r π)^{1 / 9},

then the value of

|\begin{array}{l} a_{1} & a_{2} & a_{3} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9} \end{array}|

is equal to

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

A value of

θ \in (0, \frac{π}{3}),

for which

|\begin{matrix} 1 + {c o s}^{2} θ & {s i n}^{2} θ & 4 c o s 6 θ \\ {c o s}^{2} θ & 1 + {s i n}^{2} θ & 4 c o s 6 θ \\ {c o s}^{2} θ & {s i n}^{2} θ & 1 + 4 c o s 6 θ \end{matrix}| = 0,

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

S_{r} = |\begin{matrix} 2 r & x & n (n + 1) \\ 6 r^{2} - 1 & y & n^{2} (2 n + 3) \\ 4 r^{3} - 2 n r & z & n^{3} (n + 1) \end{matrix}|,

then the value of

\sum_{r = 1}^{n} S_{r}

is independent of

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

Let m and M be respectively the minimum and maximum value values of

|\begin{matrix} \cos^{2} x & 1 + \sin^{2} x & \sin 2 x \\ 1 + \cos^{2} x & \sin^{2} x & \sin 2 x \\ \cos^{2} x & \sin^{2} x & 1 + \sin 2 x \end{matrix}|

Then the ordered pair (m, M) is equal to:

EASY

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

If $x, y, z \in R$ , then the value of the determinant

$|\begin{matrix} {(5^{x} + 5^{- x})}^{2} & {(5^{x} - 5^{- x})}^{2} & 1 \\ {(6^{x} + 6^{- x})}^{2} & {(6^{x} - 6^{- x})}^{2} & 1 \\ {(7^{x} + 7^{- x})}^{2} & {(7^{x} - 7^{- x})}^{2} & 1 \end{matrix}|$

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

Let

a - 2 b + c = 1 .

f (x) = |\begin{matrix} x + a & x + 2 & x + 1 \\ x + b & x + 3 & x + 2 \\ x + c & x + 4 & x + 3 \end{matrix}|,

then:

EASY

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

Let

A = [a_{i j}]

and

B = [b_{i j}]

be two

3 \times 3

real matrices such that

b_{i j} = {(3)}^{(i + j - 2)} a_{i j}

, where

i, j = 1,2, 3

. If the determinant of

B

81

, then determinant of

A

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

a, b, c

are roots of the equation

x^{3} + p x + q = 0,

then the value of

|\begin{array}{l} a & b & c \\ b & c & a \\ c & a & b \end{array}|

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

A = [\begin{matrix} - 4 & - 1 \\ 3 & 1 \end{matrix}]

, then the determinant of the matrix

(A^{2016} - 2 A^{2015} - A^{2014})

is :

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

y = \sin m x,

then the value of the determinant

|\begin{matrix} y & y_{1} & y_{2} \\ y_{3} & y_{4} & y_{5} \\ y_{6} & y_{7} & y_{8} \end{matrix}|

, where

y_{n} = \frac{d^{n} y}{d x^{n}}

, is

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

|\begin{matrix} a^{2} & b c & c^{2} + a c \\ a^{2} + a b & b^{2} & c a \\ a b & b^{2} + b c & c^{2} \end{matrix}| = k a^{2} b^{2} c^{2},

then

k =

HARD

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

a, b, c

are the integers between

1

and

9

and

a 51, b 41, c 31

are three-digit numbers and the value of determinant

D = |\begin{matrix} 5 & 4 & 3 \\ a 51 & b 41 & c 31 \\ a & b & c \end{matrix}|

is zero, then

a, b & c

are

EASY

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

Let

A

be a square matrix of order

3 \times 3

, then

|5 A| =

EASY

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

The value of the determinant

|\begin{matrix} a - b & b + c & a \\ b - c & c + a & b \\ c - a & a + b & c \end{matrix}|

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

A = [\begin{array}{l} 1 & 3 \\ 4 & 2 \end{array}], B = [\begin{array}{l} 2 & - 1 \\ 1 & 2 \end{array}],

then

|A B B^{'}| =

HARD

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

Let

α

and

β

be the roots of the equation

x^{2} + x + 1 = 0 .

Then for

y \neq 0

R, |\begin{matrix} y + 1 & α & β \\ α & y + β & 1 \\ β & 1 & y + α \end{matrix}|

is equal to

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Properties of Determinants

Let

a, b, c

be such that

(b + c) \neq 0

and

|\begin{matrix} a & a + 1 & a - 1 \\ - b & b + 1 & b - 1 \\ c & c - 1 & c + 1 \end{matrix}|

+ |\begin{matrix} a + 1 & b + 1 & c - 1 \\ a - 1 & b - 1 & c + 1 \\ {(- 1)}^{n + 2} a & {(- 1)}^{n - 1} b & {(- 1)}^{n} c \end{matrix}| = 0

Then the value of

n

In a third order 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 determinant, where n has the value

Important Questions on Matrices and Determinants

Learn and Prepare for any exam you want !

In a third order 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 $n$ determinant, where $n$ has the value