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

A = [ 2 -3

3 4 ]

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

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 |

^{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 ]

If elements of a row (or column) are multiplied with cofactors of any other row (or column), then their sum is zero....

So can it b applied for ANY row or column???? Can v take any row of column of our choice or just the adjacent ones??? Such as 1st row with 3rd row and like that?????

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

A 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) .If det [ p b c

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

a b r]

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????????

a

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

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

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

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

| ca cb a^2+ b^2|

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

Without expanding, show that the determinant :

1/a a

^{2}bc1/b b

^{2}ac = 01/c c

^{2}abpy+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.....

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.

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

[0 10]

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 !!

IF |A|=2,where A is a 2x2 matrix ,find |adj A|.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}265 240 219

240 225 198

219 198 181

=0

solve the system of equations

x-y+2z=1

2y-3z=1

3x-2y+4z=2

|c b-x a|

|b a c-x|

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|.

^{2}- 4A + 7I = 0 using this calculate A^{5}What is the formula for Det[ adj( adj(A) ) ] and how do you derive it ?

Evaluate the following determinants:

bar of (log

_{a}b 1)(1 log

_{b}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?

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

Pls. answer

easy way to solve elementary row or column transformation

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

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?

for what value of x is the following matrix singular

[3-2x x+1

2 4 ]

^{2}a

^{2}1 a =a a

^{2 }1 (a^{3}-1)^{2}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.

prove that determinant of x x

^{2 }yzy y

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

^{2}xya b-c c+b

a+c b c-a

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

A is a matrix of order 3 such that A (ADJA ) = 10 I then determinant adj A(a

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

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

^{2}+ a^{2})/bWithout 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 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|

prove that a+b+2c a b

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

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

Prove that

|a

^{2}a^{2}-(b-c)^{2}bc||b

^{2}b^{2}-(c-a)^{2}ca||c

^{2}c^{2}-(a-b)^{2}ab|= (a-b) (b-c) (c-a) (a+b+c) (a

^{2}+b^{2}+c^{2})Using the properties of determinants ,show that

0 p-q p-r

q-p 0 q-r

r-p r-q 0

=0..

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

4. For what value of k is the following function continuous at x = 2 ?

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!!!!!!

|sin(A+B+C) sin B cos C |

|-sinb 0 tan A | = 0,if A+B+c=pi?

|cos(A+B) -tan A 0 |