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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 |
PROVE THAT THE DETERMINANT
b2+c2 ab ac
ab c2 +a2 bc
ac bc a2+b2
is equal to 4a2b2c2
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
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|?
prove without expanding that the determinant equals 0b2c2 bc b-cc2a2 ca c-aa2b2 ab a-b
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]
Given I2. Find determinant I2. also find determinant 3I2.
state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????
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
Difference between cramer's rule and Matrix method.....and when to use which one.....
y y2 1+y3 = 0 , then show that 1+xyz = 0 ?
z z2 1+z3
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
265 240 219
240 225 198
219 198 181
prove using properties of determinants:
Xc1 Xc2 Xc3
Yc1 Yc2 Yc3 = xyz/12(x-y)(y-z)(z-x)
Zc1 Zc2 Zc3
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 ?
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
if A is a square matrix of order 3 such that adj(2A) = k adj(A) , then wite the value of k..
prove that the 3x3 determinant :
| 1+a2-b2 2ab -2b |
| 2ab 1-a2+b2 2a | = (1+a2+b2)3
| 2b -2a 1-a2-b2 |
how to solve determinant of 4x4 matrix?
If A is an invertible matrix of order 3 and |A|=5, then find |adj A|
| a^2+b^2/c c c |
| a b2+c2/a a |
|b b c2+a2/b|
IF |A|=2,where A is a 2x2 matrix ,find |adj A|.
evaluate without expansion
1 bc+ad b2c2+a2d2
1 ca+bd c2a2+b2d2
1 ab+cd a2b2+c2d2
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|
if A is an invertible matrix of order 3 and |A|=5 the find the value of |adjA|
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 prove that :-2 *determinant[ (a b c) , (a' b' c') , (a" b" c")]=
determinant [(a+b b+c c+a) , (a'+b' b'+c' c'+a'),(a"+b" b"+c" c"+a")].
(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!!!!!!
Using the properties of determinants ,show that
0 p-q p-r
q-p 0 q-r
r-p r-q 0
find the numbers a and b such that A2
+ aA + bI = O.
If det(A) = x x^3 x^4 - 1
y y^3 y^4 - 1 = 0
z z^3 z^4 - 1
Then prove that xyz(xy + yz + xz) = (x + y + z).
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