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Using properties of determinants prove that -
In this ques.. i just want to know tht after applying C1→ C1-C2, C2→ C2-C3
in this ques how can i take (a+b+c) common from C1 and C2.
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 A is a square matrix of order 3, such that / adj.A / = 64 . then find / A' / .
| (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 and / 3A / = k/A/ find value of k? pls fast plss
Prove that the following determinant is equal to (ab + bc + ca)3 :
-bc b2 + bc c2 + bc
a2 + ac -ac c2 + ac
a2 + ab b2 + ab -ab
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
x2 y2 z2
x3 y3 z3 | = xyz(x - y)(y - z)(z - x) .
2. Using properties of determinants, prove the following :
| x x2 1+px3
y y2 1+py3
z z2 1+pz3 | = (1+ pxyz)(x - y)(y - z)(z - x) .
state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????
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
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
b2+c2 ab ac
ab c2 +a2 bc
ac bc a2+b2
is equal to 4a2b2c2
265 240 219
240 225 198
219 198 181
prove that a+b+2c a b
c b+c+2a b = 2( a+b+c)3
c a c+a+2b
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 0b2c2 bc b-cc2a2 ca c-aa2b2 ab a-b
Difference between cramer's rule and Matrix method.....and when to use which one.....
for any 2*2 matrix A, if A(adjA) = [10 0] find A determinant....?
Using properties of determinats, prove that
a2 2ab b2
b2 a2 2ab
2ab b2 a2
= (a3 + b3)2
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 !!
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.
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|.
Show that the elements along the main diagonal of a skew symmetric matrix are all zero.
If the value of the third order determinant be 11,then what is value of the square of determinant formed by its cofactor?
easy way to solve elementary row or column transformation
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?
prove that the 3x3 determinant :
| 1+a2-b2 2ab -2b |
| 2ab 1-a2+b2 2a | = (1+a2+b2)3
| 2b -2a 1-a2-b2 |
| a^2+b^2/c c c |
| a b2+c2/a a |
|b b c2+a2/b|
how to solve determinant of 4x4 matrix?
If A is an invertible matrix of order 3 and |A|=5, then find |adj A|
prove that determinant of x x2 yz
y y2 zx = (x-y)(y-z)(z-x)(xy+yz+zx)
z z2 xy
Without expanding the determinant , show that | 1 a a2 | | 1 bc b+c |
| 1 b b2 | = | 1 ca c+a |
| 1 c c2 | | 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|
rn|logb q 1| =0r
| log c r 1|
(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
[y+z x y]
[z+x z x]
[x+y y z]
=(x +y+z) (x-z)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 and det adjA=64 find detA and det A -1HELP NEEDED URGENT
y y2 1+y3 = 0 , then show that 1+xyz = 0 ?
z z2 1+z3
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!!!!!!
deteminants (109 102 95
6 13 20
1 -6 -13 is equal to
the r.d sharma 2007 editn. exercise. 6.2 pg. no.6.41, qwestn numb.1 pat no. 6 plz tell no hints available.............. :(((
Using the properties of determinants ,show that
0 p-q p-r
q-p 0 q-r
r-p r-q 0
for what value of x is the following matrix singular
2 4 ]
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