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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 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 |
without expanding the determinant show that-
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 and / 3A / = k/A/ find value of k? pls fast plss
Difference between cramer's rule and Matrix method.....and when to use which one.....
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
IF 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|?
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) .
If det [ p b c
a q c = 0 then find (p/p-a) + (q/q-b) + (r/r-c)
a b r]
2.For what value of k the points (5,5),(k,1)and(11,7)are collinear(ans is k=-7)
PROVE THAT THE DETERMINANT
b2+c2 ab ac
ab c2 +a2 bc
ac bc a2+b2
is equal to 4a2b2c2
if A is a square matrix of order 3 such that adj(2A) = k adj(A) , then wite the value of k..
state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????
If A is a square matrix of order n, then
A (adj A) = (adj A) A = |A| I, where I is the identity matrix of order n
Whats "|A|" here ???
Given I2. Find determinant I2. also find determinant 3I2.
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
for any 2*2 matrix A, if A(adjA) = [10 0] find A determinant....?
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
a2 2ab b2
b2 a2 2ab
2ab b2 a2
= (a3 + b3)2
Without expanding, show that the determinant :
1/a a2 bc
1/b b2 ac = 0
1/c c2 ab
265 240 219
240 225 198
219 198 181
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 ?
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?????
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.
easy way to solve elementary row or column transformation
prove that the 3x3 determinant :
| 1+a2-b2 2ab -2b |
| 2ab 1-a2+b2 2a | = (1+a2+b2)3
| 2b -2a 1-a2-b2 |
sin 20 cos20 = -sin50
sin 70 cos70
Using the properties of determinants ,show that..
2 3 7
13 17 5
15 20 12
how to solve determinant of 4x4 matrix?
using the properties of determinants show that..
sin2x cos2x 1
cos2x sin2x 1
-10 12 2
(sin2x and cos2x means sin square x and cos square x respectively)
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
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.
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|
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
prove that a+b+2c a b
c b+c+2a b = 2( a+b+c)3
c a c+a+2b
(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 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!!!!!!
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