Write down how many pivots and how many free variables the systems has
Task 1
Reduced form of augmented matrix (extended coefficient matrix) to a linear
equation system looks like this:
(a) Write down how many pivots and how many free variables the systems
has.
(b) Write the solutions in vector form.
(c) If only one number in the matrix above was different, then the system would not have
some solution. What number is that? (Write the new matrix.)
Task 2
equation system
(a) Use row operations (Gauss-Jordan) to find the solution.
(b) Use A ^ −1 to find the solution.
(c) Use Cramer’s rule to find the solution.
Task 3
We have a linear first order differential equation
where y (0) = 2
(a) Solve as linear equation without Laplace.
(b) Solve with Laplace Transform.
Task 4
A function f is given at
- Find the partial derivative of fof first and second order.
- Find and classify the critical points of f
Task 5
We look at the matrix
(a) Find A^-1 using cofactor expansion.
(b) Find A^-1 using row operations.
Exercise 6
We shall solve the homogeneous system of differential equations
(a) Solve by diagonalizing the matrix.
(b) Solve with Laplace Transform