problem:
a) Given that k is a constant, find which of these equations are linear.
i) x_{1} – x_{2} + x_{3} = sin k,
ii) kx_{1} – (1/k) x^{2} = 9,
iii) 2^{k} sinx_{1} – x_{2} + x_{3}^{2} = 0
b) Find the augmented matrix of the following system of linear equations:
2x_{1} + 2x_{3} = 1
3x_{1} – x_{2} + 4x_{3} = 7
6x_{1} + x_{2} – x_{3} = 0
problem:
a) Consider the following system of linear equations:
x + y + 2z = a
x + z = b
2x + y + 3z = c
Show that for this system to be consistent, the constants must satisfy the condition: c = a+ b
b) prepare the definition of a reduced-row-echelon form matrix. prepare which of the following matrices are in the row-echelon and which are in the reduced row echelon forms.
problem: Solve the following system of lonear equation by Gauss-Jordan elimination method.
x_{1} + x_{2 }+ 2x_{3} = 8
-x_{1} – 2x_{2} + 3x_{3} = 1
3x_{1} – 7x_{2} + 4x_{3} = 10
problem: Solve the following system of linear equations for λ = 1 and 2.
2x_{1} – x_{2} = λ x_{1}
2x_{1} – x_{2} + x_{3} = λ x_{2}
2x_{1} – 2x_{2} + x_{3} = λ x_{3}