For each system of equations: a) Express the equations in matrix form, identifying the matrix A of coefficients. b) Calculate the kernel and image of the matrix A. c) You should choose an appropriate method for each set of equations (using each method once) from the following methods you have learnt Solve the equations, where possible giving the most general solution when there are infinitely many solutions. If no solution can be found, explain why. d) Relate your space of solutions or lack of it to the answer to b). Inverse matrix method (the inverse should be generated via the adjoint matrix) ● Gaussian Elimination Gauss-Jordan Elimination • Cramer's Rule (i) You must show your working. (ii) 4x + y - 2z = a x - 5y + 2z = b 2x + y + 4z = C 10x - 2y + z = b x+8y-3z = c 2x+y-6z = d
For each system of equations: a) Express the equations in matrix form, identifying the matrix A of coefficients. b) Calculate the kernel and image of the matrix A. c) You should choose an appropriate method for each set of equations (using each method once) from the following methods you have learnt Solve the equations, where possible giving the most general solution when there are infinitely many solutions. If no solution can be found, explain why. d) Relate your space of solutions or lack of it to the answer to b). Inverse matrix method (the inverse should be generated via the adjoint matrix) ● Gaussian Elimination Gauss-Jordan Elimination • Cramer's Rule (i) You must show your working. (ii) 4x + y - 2z = a x - 5y + 2z = b 2x + y + 4z = C 10x - 2y + z = b x+8y-3z = c 2x+y-6z = d
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
A is 1, B is 2, C is 9, D is 3
Transcribed Image Text:On the next page there are four separate systems of linear equations, where a, b, c and d are the first
four digits of your code number.
For each system of equations:
a) Express the equations in matrix form, identifying the matrix A of coefficients.
b) Calculate the kernel and image of the matrix A.
c) Solve the equations, where possible giving the most general solution when
there are infinitely many solutions. If no solution can be found, explain why.
Relate your space of solutions or lack of it to the answer to b).
d)
You should choose an appropriate method for each set of equations (using each method once) from
the following methods you have learnt
Inverse matrix method (the inverse should be generated via the adjoint matrix)
● Gaussian Elimination
● Gauss-Jordan Elimination
Cramer's Rule
●
You must show your working.
(i)
(ii)
(iii)
(iv)
4x + y - 2z = a
x - 5y + 2z = b
2x + y + 4z = c
10x - 2y + z = b
x+8y-3z = c
2x + y - 6z = d
2x + 5y-z = a
3x + 2y + 2z = b
5x + 7y+z= a + b + 1
x + 4y + 2z = c
2x - 5y + z = d
3x-y + 3z = c+d
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