Using properties of determinants, prove the following |(3a,-a+b,-a | Filo

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Class 12 Math Algebra Determinants

Using properties of determinants, prove the following

∣ ∣ ∣ ∣ ∣ ∣ ∣ 3 a a - b a - c - a + b 3 b b - c - a + c c - a 3 c ∣ ∣ ∣ ∣ ∣ ∣ ∣ = 3 (a + b + c) (a b + b c + c a)

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Similar topics

determinants

matrices

binomial theorem

complex numbers and quadratic equations

sequences and series

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determinants

matrices

binomial theorem

complex numbers and quadratic equations

sequences and series

Related Questions

The points (-a, -b), (0, 0), (a, b) and (

a^{2}

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Find equation of line joining (1,2) and (3,6) using determinants.

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y - x = 5, 3 x + 4 y = 1

y = m x + 3

are concurrent then the value of m is

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∣ ∣ ∣ ∣ ∣ ∣ ∣ x_{1} x_{2} x_{3} y_{1} y_{2} y_{3} 111 ∣ ∣ ∣ ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ ∣ ∣ ∣ 1 b_{1} a_{1} 1 b_{2} a_{2} 1 b_{3} a_{3} ∣ ∣ ∣ ∣ ∣ ∣ ∣

then the two triangles whose vertices are

(x_{1}, y_{1}), (x_{2}, y_{2}), ((x_{3}, y_{3})

(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{13}, b_{3}),

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Number of values of

a

for which the lines

2 x + y - 1 = 0, a x + 3 y - 3 = 0, 3 x + 2 y - 2 = 0

are concurrent is

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Show that the points

A (- 7, 4, - 2), B (- 2, 1, 0)

C (3, - 2, 2)

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If the points (-3,6), (-9,a) and (0,15) are collinear, then find a.

play button image

x_{1}, x_{2}, x_{3}

y_{1}, y_{2}, y_{3}

are in G.P. with same common ratio, then the points

P (x_{1}, y_{1}), Q (x_{2}, y_{2})

R (x_{3}, y_{3})

play button image

Related Questions

The points (-a, -b), (0, 0), (a, b) and (

a^{2}

play button image

Find equation of line joining (1,2) and (3,6) using determinants.

play button image

y - x = 5, 3 x + 4 y = 1

y = m x + 3

are concurrent then the value of m is

play button image

∣ ∣ ∣ ∣ ∣ ∣ ∣ x_{1} x_{2} x_{3} y_{1} y_{2} y_{3} 111 ∣ ∣ ∣ ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ ∣ ∣ ∣ 1 b_{1} a_{1} 1 b_{2} a_{2} 1 b_{3} a_{3} ∣ ∣ ∣ ∣ ∣ ∣ ∣

then the two triangles whose vertices are

(x_{1}, y_{1}), (x_{2}, y_{2}), ((x_{3}, y_{3})

(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{13}, b_{3}),

play button image

Number of values of

a

for which the lines

2 x + y - 1 = 0, a x + 3 y - 3 = 0, 3 x + 2 y - 2 = 0

are concurrent is

play button image

Show that the points

A (- 7, 4, - 2), B (- 2, 1, 0)

C (3, - 2, 2)

play button image

If the points (-3,6), (-9,a) and (0,15) are collinear, then find a.

play button image

x_{1}, x_{2}, x_{3}

y_{1}, y_{2}, y_{3}

are in G.P. with same common ratio, then the points

P (x_{1}, y_{1}), Q (x_{2}, y_{2})

R (x_{3}, y_{3})

play button image

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Home
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Copyright FILO EDTECH PVT. LTD. 2021