Mathematics>Algebra>Matrices and Determinants>Determinants

MEDIUM

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If $A = |\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}|$ , find determinants using Sarrus Rule.

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Important Questions on Matrices and Determinants

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Determinants

If area of triangle is

35 sq . units

with vertices

(2, - 6), (5, 4)

and

(k, 4)

, then

k =

_____

EASY

Mathematics>Algebra>Matrices and Determinants>Determinants

Let

A (a, 0), B (b, 2 b + 1)

and

C (0, b), b \neq 0, | b | \neq 1

, be points such that the area of triangle

A B C

is

1

sq. unit, then the sum of all possible values of

a

is:

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Determinants

If area of a triangle whose vertices are

(8, 2), (k, 4)

and

(6, 7)

is

13

units then the possible integer value of

k

is

EASY

Mathematics>Algebra>Matrices and Determinants>Determinants

Find the area of the triangle whose vertices are

(- 2, - 3), (3, 2) and (- 1, - 8)

using determinant method.

EASY

Mathematics>Algebra>Matrices and Determinants>Determinants

If the matrix

[\begin{matrix} 1 & 2 & - 1 \\ - 3 & 4 & k \\ - 4 & 2 & 6 \end{matrix}]

is singular, then the value of

k

is equal to

EASY

Mathematics>Algebra>Matrices and Determinants>Determinants

Find the area of the triangle whose vertices are

(- 2, - 3), (3, 2) and (- 1, - 8)

by using determinant method.

EASY

Mathematics>Algebra>Matrices and Determinants>Determinants

Using determinants, find the values of

k

, if the area of triangle with vertices

(- 2, 0), (0, 4) and (0, k)

is

4

square units.

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Determinants

Find the area of triangle whose vertices are

(- 1, 1, 2), (1, 2, 3), (2, 5, - 1)

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Determinants

If

ω

is a complex cube root of unity, then the matrix

A = [\begin{matrix} 1 & ω^{2} & ω \\ ω^{2} & ω & 1 \\ ω & 1 & ω^{2} \end{matrix}]

is a

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Determinants

If the area of the triangle with vertices

(2, 5), (7, k) & (3, 1)

is

10

, then find the value of

k

.

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Determinants

Find the area of the triangle with vertices

(2, 7), (1, 1)

and

(10, 8)

using determinant method.

HARD

Mathematics>Algebra>Matrices and Determinants>Determinants

Let two points be

A (1, - 1)

and

B (0, 2) .

If a point

P (x^{'}, y^{'})

be such that the area of

∆ P A B = 5

sq. units and it lies on the line

3 x + y - 4 λ = 0,

then a value of

λ

is

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Determinants

The value of

x

for which the matrix

[\begin{matrix} 8 & x & 0 \\ 4 & 0 & 2 \\ 12 & 6 & 0 \end{matrix}]

is singular, is -

EASY

Mathematics>Algebra>Matrices and Determinants>Determinants

The vectors

\vec{a} = \hat{i} + \hat{j} + m \hat{k}, \vec{b} = \hat{i} + \hat{j} + (m + 1) \hat{k}

and

\vec{c} = \hat{i} - \hat{j} + m \hat{k}

are coplanar

HARD

Mathematics>Algebra>Matrices and Determinants>Determinants

If area of

∆ A B C

is

12

square units and vertices are

A (x, 2), B (4, 1)

and

C (- 3, 7)

, then the positive value of

x

.

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Determinants

If the area of the triangle, whose vertices are

(2, - 6), (5, 4)

and

(k, 4)

is

35

square unit, then find the value of

k

.

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Determinants

The vertices of a triangle

ABC

are given by position vector

A (\hat{i} + \hat{j} + 2 \hat{k}), B (2 \hat{i} + 3 \hat{j} + 5 \hat{k})

and

C (\hat{i} + 5 \hat{j} + 5 \hat{k})

. Find its area.

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Determinants

The points

(k, 2 - 2 k), (- k + 1, 2 k)

and

(- 4 - k, 6 - 2 k)

are collinear for

EASY

Mathematics>Algebra>Matrices and Determinants>Determinants

Three vertices of

∆ A B C

are

A (1, 4), B (- 2, 2)

and

C (3, 2) .

Then the area of

∆ A B C

is

HARD

Mathematics>Algebra>Matrices and Determinants>Determinants

If area of triangle is

35

sq. units with vertices

(2, - 6), (5, 4)

and

(k, 4),

then

k

is