if (-2 1 x+2 )
(3 x-4 5 ) =25
(0 1 3 )
p/s : all the value above in one bracket ( )
a) find the value of x
b) hence ,find (-2 1 x+2 )^-1
( 3 x-4 5 )
(o 1 3 )
p/s : all the value above in one bracket ( )
I assume you meant the determinant
24 x + 3 x^2 + 6 x + 10 - 9x = 25
3 x^2 + 21 x -15 = 0
x^2 + 7 x - 5 = 0
x =-7/2 +/- (1/2) sqrt(69)
What a mess, assume you have a typo.
To invert matrix use
http://matrix.reshish.com/inverse.php
To find the value of x in the given equation:
1) Multiply the matrices on the left-hand side of the equation:
(-2 1 x+2) (3 x-4 5) = 25 (0 1 3)
This can be written as the following equation:
-2(3) + 1(x-4) + (x+2)(5) = 25 + 0 + 3
-6 + x - 4 + 5x + 10 = 28
Combine like terms:
6x = 28 - 6 - 10 + 4
6x = 16
Divide both sides by 6:
x = 16/6
Simplifying the fraction:
x = 8/3
a) The value of x is 8/3.
Now, to find the inverse of the matrix (-2 1 x+2) (3 x-4 5) (0 1 3):
b) To find the inverse of a matrix, we can use the following general formula:
A^(-1) = (1/det(A)) * adj(A)
First, we need to find the determinant of the matrix A.
det(A) = (-2*(x-4)*3) + (1*(5)*(0)) + ((x+2)*(1)*(3))
= (-6x + 24) + 0 + (3x + 6)
= -6x + 3x + 24 + 6
= -3x + 30
Now, let's find the adjoint of the matrix A.
To find the adjoint of a 3x3 matrix, interchange each element of the main diagonal (top-left to bottom-right), and change the sign of each element in the other diagonal (top-right to bottom-left).
The matrix A is:
(-2, 1, x+2)
(3, x-4, 5)
(0, 1, 3)
The adjoint of A is:
((x-4), -(1), 1(-2))
(-1(3), 1(3), -2)
(1, 3(2), -(x-4))
Simplifying the adjoint, we get:
(x-4, -1, -2)
(-3, 3, -2)
(1, 6, 4-x)
Now, combine the determinant and adjoint to find the inverse.
A^(-1) = (1/(-3x+30)) * (x-4, -1, -2)
(-3, 3, -2)
(1, 6, 4-x)
This is the inverse of the matrix (-2 1 x+2) (3 x-4 5) (0 1 3).
Please note that the solution of x may be different or invalid depending on the context of the problem, as it requires additional information.