Q1. Use Gaussian elimination to solve the system of linear equations: X1 2x2 6x3 10 2x₁ + 3x₂ + 12x3 -12 2x₁ - 4x₂ 12x3 20 = = =

College Algebra (MindTap Course List)
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Author:R. David Gustafson, Jeff Hughes
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Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 86E
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Q1. Use Gaussian elimination to solve the system of linear equations:
х1 - 2х2 - 6х3
=
10
2x₁ + 3x₂ + 12x₂ = -12
2x₁ - 4x₂
12x3
20
Q2. Solve the system equations using Cramer's Rule.
3x-2y+z=9
x+2y-2z = -5
x+y=4z=-2
Q3. If A
=
[2
4
=
4
41
2 4 show that A² -8A - 201=0 where 1,0 are the unit matrix and
4 4 2
the null matrix of order 3 respectively. Use this result to find A-¹.
Q4. Find the inverse of the A matrix using Gauss-Jordan elimination method.
[35 7
-1
4
A = 1 2
L2 6
Transcribed Image Text:Q1. Use Gaussian elimination to solve the system of linear equations: х1 - 2х2 - 6х3 = 10 2x₁ + 3x₂ + 12x₂ = -12 2x₁ - 4x₂ 12x3 20 Q2. Solve the system equations using Cramer's Rule. 3x-2y+z=9 x+2y-2z = -5 x+y=4z=-2 Q3. If A = [2 4 = 4 41 2 4 show that A² -8A - 201=0 where 1,0 are the unit matrix and 4 4 2 the null matrix of order 3 respectively. Use this result to find A-¹. Q4. Find the inverse of the A matrix using Gauss-Jordan elimination method. [35 7 -1 4 A = 1 2 L2 6
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