Solve the following linear system of equations using Gaussian Elimination method (1-2):
1.
x + 2y + 3z = 3
2x + 3y + 8z = 4
5x + 8y + 19z = 11
2.
x1 − x2 + x3 − x4 + x5 = 1
2x1 − x2 + 3x3 + 4x5 = 2
3x1 − 2x2 + 2x3 + x4 + x5 = 1
x1 + x3 + 2x4 + x5 = 0
Solve the following linear system of equations using Gauss-Jordan Elimination method (3-4):
3.
x + 2y − 3z = 4
x + 3y + z= 11
2x + 5y − 4z = 13
2x + 6y + 2z = 22
4.
10x2 − 4x3 + x4 = 1
x1 + 4x2 − x3 + x4 = 2
3x1 + 2x2 + x3 + 2x4 = 5
−3x1 − 8x2 + 2x3 − 2x4 = −4
x1 − 6x2 + 3x3 = 1
5. Forward elimination changes Ax = b to a row reduced Rx = d ; the general solution is
x=(4 0 0) + s92 1 0)+ t(5 0 1)
What is the 3 × 3 reduced row echelon matrix R and what is d?
11. Suppose
A(t) =[ e^t 0 0
0 cost sint
0 −sint cost]
,show that A(t)^-1 exists and then find it.
Solve the following linear system of equations using Inverse matrix method (12-13):
12.
x + y + z = 6
2x + 3y + 4z = 20
3x − 2y + z = 2
13.
x + y + z − 2t = −4
x − 2y + 3z + 4t = 10
2x + 3y − z + 2t = 9
4x − y + 2z − t = −7
14. If � = 5
3 2 1
4 −1 2
7 3 −3
14. If A=[3 2 1 4 -1 2 7 3 -3], find A^-1 and hence solve the system of equations,
3x + 4y + 7z = 14
2x − y + 3z = 4
x + 2y − 3z = 0
15. If A =[x+y y+z z+x z x y 1 1 1] then compute the determinant of A
16. By using the properties of determinant prove that
|b62+c^2 a^2 a^2 b^2 c^2+a^2 b^2 c^2 c^2 a^2+b^2|=4a^2b^2c^2
17. find the determinant using the row operations |1 2 1 2 3 1 -2 3 -1 0 3 1 2 3 2 -1|
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
