Solve the system using Gaussian elimination

Question

Answer 1

(1)

Step 1:

The system of linear equations are 

Write the equations into matrix form .

 is coefficient matrix,  is variable matrix and  is constant matrix.

Solve the equations in Gaussian elimination method.

The augmented matrix is .

  are represents first row and second row.

Eliminate second row and first coloumn.

Eliminate first row and second coloumn.

Solution:

The system of equations values are 

Answer 2

(2)

The addition matrix is

Simplify the matrix operation.

Answer 3

(3)
The matrix 

Find .

The first matrix is  and second matrix is , So its multipication possible.

Answer 4

(4)

The equation is 

Identify the conic section equation.

The conic section equation is 

Answer 5

(5)

Step 1:

The infinite sequence of recursion formula is

Find the first four terms.

Substitute  in the recursion formula.

Substitute  in the recursion formula.

Substitute  in the recursion formula.

Substitute  in the recursion formula.

Find eight term.

Substitute  in the recursion formula.

Solution:

The infinite sequences of first four and eighth terms,