Gaussian Elimination and a couple trig questions

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,