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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}.If det [ p b c

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

a b r]

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

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,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 ]

^{3}- b^{3}-c^{3}if a is a square matrix of order 3 and / 3A / = k/A/ find value of k? pls fast plss

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 -abA matrix of order 3X3 has determinant 5. What is the value of |3A|?

1. 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) .sin^2A cotA 1

sin^2B cotB 1 =0

sin^2C cotC 1

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}state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????

| b^2 +c^2 ab ac |

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

| ca cb a^2+ b^2|

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

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

prove without expanding that the determinant equals 0

b2c2 bc b-c

c2a2 ca c-a

a2b2 ab a-b

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.....

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

for any 2*2 matrix A, if A(adjA) = [10 0] find A determinant....?

[0 10]

Mr. X has invested a part of his investment in 10% bond A and a part in 15% bond B. His interest income during first year is Rs. 4000. If he invests 20% more in 10% bond A and 10% more in 15% bond B, his income during the second year increases by Rs. 500. Find his initial investment using matrix method

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 !!

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}^{2}A sinA cos A cos^{2}A], r2=[sin^{2}B sinB cos B cos^{2}B] and r3=[sin^{2}C sinC cosC cos^{2}C] = -sin(A-B) sin(B-C) sin(C-A).px+y x y

py+z y z = 0

0 px+y py+z

^{2}a

^{2}1 a =a a

^{2 }1 (a^{3}-1)^{2}265 240 219

240 225 198

219 198 181

=0

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

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

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?

|x p q|

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

|q q x|

easy way to solve elementary row or column transformation

^{2} θ cot^{2}θ 1) (cot^{2}θ cosec^{2}θ -1) (42 40 2)| = 0Show that the elements along the main diagonal of a skew symmetric matrix are all zero.

Pls. answer

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}|if A is a square matrix such that A

^{2}= I what is the inverse of A? ans fast needed its urgent plssssshow to solve determinant of 4x4 matrix?

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

^{2}1+y^{3}= 0 , then show that 1+xyz = 0 ?z z

^{2}1+z^{3}If A is an invertible matrix of order 3 and |A|=5, then find |adj A|

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

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

^{2}+ a^{2})/ba b-c c+b

a+c b c-a

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

x b z detminant =0 prove that

x y c

a/a-x +b/b-y + c/c-z=2

prove that determinant of x x

^{2 }yzy y

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

^{2}xyShow that

[y+z x y]

[z+x z x]

[x+y y z]

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

^{2}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|

|c b-x a|

|b a c-x|

Using the properties of determinants ,show that

0 p-q p-r

q-p 0 q-r

r-p r-q 0

=0..

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.

prove that a+b+2c a b

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

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

$\left|\begin{array}{ccc}yz-{x}^{2}& zx-{y}^{2}& xy-{z}^{2}\\ zx-{y}^{2}& xy-{z}^{2}& yz-{x}^{2}\\ xy-{z}^{2}& yz-{x}^{2}& zx-{y}^{2}\end{array}\right|$ is divisible by (

x + y + z), and hence find the quotient.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

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|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!!!!!!

if A is a square matrix of order 3 and det adjA=64 find detA and det A

^{-1}HELP NEEDED URGENTthe r.d sharma 2007 editn. exercise. 6.2 pg. no.6.41, qwestn numb.1 pat no. 6 plz tell no hints available.............. :(((

for what value of x is the following matrix singular

[3-2x x+1

2 4 ]