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Syllabus

Using properties of determinants prove that -

(b+c)

^{2}....a^{2}........a^{2}b

^{2}.....(c+a)^{2.}.....b^{2}=2abc(a+b+c)^{3}c

^{2}.....c^{2}.......(a+b)^{2}In this ques.. i just want to know tht after applying C

_{1}→ C_{1}-C_{2}, C_{2}→ C_{2}-C_{3}in this ques how can i take (a+b+c) common from C

_{1}and C_{2}.Prove that

| (b+c)^2 a^2 a^2 |

| b^2 (c+a)^2 b^2 | = 2abc(a+b+c)^3

| c^2 c^2 (a+b)^2 |

if A is a square matrix of order 3, such that / adj.A / = 64 . then find / A' / .

Without expanding, show that the determinant :

1/a a

^{2}bc1/b b

^{2}ac = 01/c c

^{2}ab^{3}- b^{3}-c^{3}If a,b,c, all positive ,are pth,qth and rth terms of G.P. , prove that determinant [ log a p 1

log b q 1 = 0

log c r 1 ]

5.Three schools A, B and C want to award their selected students for the values of honesty, regularity and hard work. Each school decided to award a sum of Rs. 2500, Rs. 3100, Rs. 5100 per student for the respective values. The number of students to be awarded by the three schools as given below:A = 50500, 40800, 41600

if a is a square matrix of order 3 and / 3A / = k/A/ find value of k? pls fast plss

= 2(a+b)(b+c)(c+a)

Prove that the following determinant is equal to (ab + bc + ca)

^{3 :}-bc b

^{2}+ bc c^{2}+ bca

^{2}+ ac -ac c^{2}+ aca

^{2}+ ab b^{2}+ ab -ab1. Using properties of determinants, prove the following:

| x y z

x

^{2}y^{2}z^{2}x

^{3}y^{3}z^{3 | = }xyz(x - y)(y - z)(z - x) .2. Using properties of determinants, prove the following :

| x x

^{2}1+px^{3}y y

^{2}1+py^{3}z z

^{2}1+pz^{3}| = (1+ pxyz)(x - y)(y - z)(z - x) .A matrix of order 3X3 has determinant 5. What is the value of |3A|?

| x+a b c|

| b. x+c. a|. =. 0 is -(a+b+c).

| c. a x+b|

265 240 219

240 225 198

219 198 181

=0

a

^{2}2ab b^{2}b

^{2}a^{2}2ab = (a^{3}+b^{3})^{2}2ab b

^{2}a^{2}If det [ p b c

a q c = 0 then find (p/p-a) + (q/q-b) + (r/r-c)

a b r]

^{2}a

^{2}1 a =a a

^{2 }1 (a^{3}-1)^{2}PROVE THAT THE DETERMINANT

b

^{2}+c^{2}ab acab c

^{2}+a^{2 }bcac bc a

^{2}+b^{2}is equal to 4a

^{2}b^{2}c^{2}-1010-4040state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????

{1 a2+bc a3

1 b2+ca b3

1 c2+ab c3} = -(a-b) (b-c) (c-a) (a2 +b2+c2) using properties of determinannts solve

(a

^{2}+ b^{2})/c c ca (b

^{2}+ c^{2})/a a = 4abcb b ( c

^{2}+ a^{2})/b| b^2 +c^2 ab ac |

| ab c^2+a^2 bc |=4a^2b^2c^2

| ca cb a^2+ b^2|

prove without expanding that the determinant equals 0

b2c2 bc b-c

c2a2 ca c-a

a2b2 ab a-b

Using properties of determinants, solve the following for x :

x-2 2x-3 3x-4

x-4 2x-9 3x-16 =0

x-8 2x-27 3x-64

if A is a square matrix of order 3 such that adj(2A) = k adj(A) , then wite the value of k..

py+z y z

0 px+y py+z

= 0

where p is any real number

|b+c a a |

| b c+a b |=4abc

| c c a+b |

Difference between cramer's rule and Matrix method.....and when to use which one.....

Using properties of determinats, prove that

a

^{2 }2ab b^{2}b

^{2 }a^{2 }2ab2ab b

^{2 }a^{2 }= (a

^{3}+ b^{3})^{2}for any 2*2 matrix A, if A(adjA) = [10 0] find A determinant....?

[0 10]

|x p q|

|p x q| =(x-p)(x^2+px-2q^2)

|q q x|

Please solve the following determinant based question | (y+z)^2 xy zx |

| xy (x+z)^2 yz | = 2xyz(x+y+z)^3 .

| xz yz (x+y)^2 |

Please give the answer fast !!

px+y x y

py+z y z = 0

0 px+y py+z

1. A square matrix A, of order 3, has |A|=5, find |A adj. A|.

What is the formula for Det[ adj( adj(A) ) ] and how do you derive it ?

Show that

[y+z x y]

[z+x z x]

[x+y y z]

=(x +y+z) (x-z)

^{2}An amount of Rs. 10,000 is put into three investments at the rate of 10,12 and 15 per cent per annum. The combined income is Rs. 1,310 and the combined income of the first and the second investment is Rs. 190 short of the income from the third.

i) Represent the above situation by matrix equation and form the linear equation using multiplication.

ii) Is it possible to solve the system of equations so obtained using matrices?

Using the properties of determinants ,show that

0 p-q p-r

q-p 0 q-r

r-p r-q 0

=0..

Show that the elements along the main diagonal of a skew symmetric matrix are all zero.

Pls. answer

Without expanding the determinant , show that

|1 a a| |^{2}1 bc b+c||1 b b^{2}|=|1 ca c+a||1 c c| |^{2}1 ab a+b|easy way to solve elementary row or column transformation

prove that the 3x3 determinant :

| 1+a

^{2}-b^{2}2ab -2b || 2ab 1-a

^{2}+b^{2}2a | = (1+a^{2}+b^{2})^{3 }| 2b -2a 1-a

^{2}-b^{2}|how to solve determinant of 4x4 matrix?

If A is an invertible matrix of order 3 and |A|=5, then find |adj A|

An amount of Rs. 50,000 is put into three investments at the rate of 6%,7% and 8% per annum respectively. The total annual income is Rs. 3,580. If the combined annual income from the first two investments is Rs. 700 more than the income from the third.

i) Represent the above situation by matrix equation and form linear equations using matrix multiplication.

ii) Is it possiblt to solve the system of equations so obtaines using matrices.

subscriber. She proposes to increase the annual subscription charges and it is believed that for

every increase of Re 1, one subscriber will discontinue. What increase will bring maximum

income to her? Make appropriate assumptions in order to apply derivatives to reach the

solution. Write one important role of magazines in our lives.

A = [ 2 -3

3 4 ]

satisfies the equation x^2 - 6x + 17 = 0. Hence find A^-1.

a b-c c+b

a+c b c-a

a-b b+a c =(a+b+c)(a^2+b^2+c^2)

|x1 y1 2 |^2

|x2 y2 2| = 3a^4

|x3 y3 2|

prove that determinant of x x

^{2 }yzy y

^{2}zx = (x-y)(y-z)(z-x)(xy+yz+zx)z z

^{2}xydsing properties of determinant prove that :- determinant [ (mC1 mC2 mC3) , (nC1 nC2 nC3),(pC1 pC2 pC3)]= {mpn(m-n)(n-p)(p-m)}/12. determinant is of order 3*3 .

A is a square matrix of order 3 and det. A = 7. Write the value of adj A.

Please give me any formula or method for calculating this problem.

| 2 5 8 |

|a23 b53 c83 |

| a b c |

if a,b,c are all positive and are pth,qth,rth terms of a G.P, then show that determinant

|log a p 1|

| log c r 1|

Using the properties of determinants, prove that:

1 bc bc(b+c)

1 ca ca(c+a) = 0

1 ab ab(a+b)

prove that a+b+2c a b

c b+c+2a b = 2( a+b+c)

^{3}c a c+a+2b

Evaluate the following determinants:

bar of (log

_{a}b 1)(1 log

_{b}a)|10! 11! 12!|

|11! 12! 13!|

|12! 13! 14!|

Solve:

(i) x+y-2z =0 (ii)2x+3y+4z =0 (iii)3x+y+z =0 (iv) x+2y-3z = -4

2x+y-3z =0 x+y+z =0 x-4y+3z =02x+3y+2z =2

5x+4y-9z =0 2x-y+3z =0 2x+5y-2z =0 3x-3y-4z =11

IF POINTS ( 2,0 ) ( 0, 5) AND ( X, Y ) ARE COLLINEAR THEN SHOW THAT X/2 + Y/5 = 1

If x + y + z = 0, prove that|xa yb zc| |a b c||yc za xb|= xyz |c a b||zb xc ya| |b c a|

Iwant the answer within 2 hours.Please!!!!!!

Using determinants prove the following points are collinear..

Using the properties of determinants, prove that:

1 x x

^{3}1 y y

^{3 }=(x-y) (y-z) (z-x) (x+y+z)1 z z

^{3}