Call me

Have a Query? We will call you right away.

+91

E.g: 9876543210, 01112345678

We will give you a call shortly, Thank You

Office hours: 9:00 am to 9:00 pm IST (7 days a week)

What are you looking for?

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(2A) = k adj(A) , then wite the value of k..

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 |

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

^{3}- b^{3}-c^{3}Solve this :$2.\mathrm{If}{\mathrm{D}}_{1}=\left|\begin{array}{ccc}{\mathrm{ab}}^{2}-{\mathrm{ac}}^{2}& {\mathrm{bc}}^{2}{\mathrm{a}}^{2}\mathrm{b}& {\mathrm{a}}^{2}\mathrm{c}-{\mathrm{b}}^{2}\mathrm{c}\\ \mathrm{ac}-\mathrm{ab}& \mathrm{ab}-\mathrm{bc}& \mathrm{bc}-\mathrm{ac}\\ \mathrm{c}-\mathrm{b}& \mathrm{a}-\mathrm{c}& \mathrm{b}-\mathrm{a}\end{array}\right|{\mathrm{D}}_{2}=\left|\begin{array}{ccc}1& 1& 1\\ \mathrm{a}& \mathrm{b}& \mathrm{c}\\ \mathrm{bc}& \mathrm{ac}& \mathrm{ab}\end{array}\right|,\mathrm{then}{\mathrm{D}}_{1}{\mathrm{D}}_{2}\mathrm{is}\mathrm{equal}\mathrm{to}-\phantom{\rule{0ex}{0ex}}\left(\mathrm{a}\right)0\left(\mathrm{b}\right){\mathrm{D}}_{1}^{2}\left(\mathrm{c}\right){\mathrm{D}}_{2}^{2}\left(\mathrm{d}\right){\mathrm{D}}_{2}^{3}$

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 ]

| x+a b c|

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

| c. a x+b|

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

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

Without expanding, show that the determinant :

1/a a

^{2}bc1/b b

^{2}ac = 01/c c

^{2}abdeterminant {5

^{2}5^{3}5^{4}5

^{3}5^{4}5^{5}5

^{4}5^{5}5^{6}}find the value of determinant1. 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) .|2 y 3|

|1 1 z|

xyz=80 and 3x+2y+10z=20

Find value of A(adjA)

If det [ p b c

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

a b r]

[1 0 1] [c-b c+a a-b]

[1 1 0] [b-c a-c a+b]

show that ABA

^{-1 }is a diagonal matrix .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}solve the following equation:

15-2x 11 10

11-3x 17 16 = 0

7-x 14 13

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

| 2 5 8 |

|a23 b53 c83 |

| a b c |

| b^2 +c^2 ab ac |

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

| ca cb a^2+ b^2|

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

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

^{T}|py+z y z

0 px+y py+z

= 0

where p is any real number

For what values of a and b, the following system of equations is consistent?

x+y+z=6

2x+5y+az=b

x+2y+3z=14 [by matrix method]

|b+c a a |

| b c+a b |=4abc

| c c a+b |

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

[0 10]

{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

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 !!

265 240 219

240 225 198

219 198 181

=0

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}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?????

A = [ 2 -3

3 4 ]

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

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|.

Q. Find minors and cofactors of all the elements of determinant $\left[\begin{array}{cc}1& -2\\ 4& 3\end{array}\right]$

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

_{r }= |1 r 2^{r }||2 n n

^{2 }||n n(n+1)/2 2

^{n+1 }|Find, summation (delta)r

r = 1 to n

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?

Evaluate the following determinants:

bar of (log

_{a}b 1)(1 log

_{b}a)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

Q.(ii) If A = $\left|\begin{array}{ccc}5& 6& -3\\ -4& 3& 2\\ -4& -7& 3\end{array}\right|$, then write the cofactor of the element ${a}_{21}$ of its 2nd row.

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?

in properties of determinants how do we apply c1-c1+c2+c3 or ri-r1+r2+r3 in any row or column plz xplain wid an example

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.

ba c2+a2 bc

ca cb a2+b2

a b-c c+b

a+c b c-a

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

Evaluate

1 a bc

1 b ca

1 c ab

[ans...value of the determinant is ab(b-a)+bc(c-b)+ac(a-c) ]

prove that determinant of x x

^{2 }yzy y

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

^{2}xythe management committe of a residential colony decided to award some of its members ( say x ) for honesty, some ( say y ) for helping others and some others ( say z ) for supervising the workers to keep the colony neat and clean.The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the no. of awardees for honesty is 33. If the sum of the no. of awardees for honesty and supervision is twice the no. of awardees for helping others, using matrix method.

Find the no. of awardees of each category.

apart from these values, suggest one more value which the management of the colony must include for awaards.

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.

(a

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

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

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

|x1 y1 2 |^2

|x2 y2 2| = 3a^4

|x3 y3 2|

prove that a+b+2c a b

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

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

a

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

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

^{2}a^{2}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

|43 3 6|

|35 21 4|=0

|17 9 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!!!!!!

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|iii). $\left[\begin{array}{ccc}x+1& -3& 4\\ -5& x+2& 2\\ 4& 1& x-6\end{array}\right]$