Solve the system of linear equations

Reference no: EM132402902

Question 1 - One step of Gaussian elimination (without pivoting) has been performed on a linear system. The linear system is shown below:

The next stage in the elimination process would be:

A. E₃ → 4E₃ - 7 E₂, E₄ → 2E₄ - E₂.

B. Interchange equations 2 and 3.

C. Interchange equations 2 and 4.

D. E₃ → E₃ - (7/4) E₂, E₄ → E₄ - ½ E₂.

E. E₃ → E₃ - (7/4)E₂, E₄ → 7E₄ - 2E₃.

F. None of these.

Question 2 - Use Gaussian elimination with partial pivoting to solve the system of linear equations. Do not use Gauss-Jordan elimination. Use exact arithmetic.

x₁ + 2x₂ + 2x₃ + 2x₄ = 0

2x₁ + 4x₂ + 3x₃ = -5

2x₂ + x₃ + 3x₄ = -2

x₂ + 3x₃ - 2x₄ = -2

Enter each component of the right hand side vector after completion of the upper triangularization of the linear system: (g₁, g₂, g₃, g₄), and, enter each component of the final solution after completion of the backward substitution stage (x₁, x₂, x₃, x₄).

Enter each component as an exact expression.

For example: -2/3 OR -45 OR 2

Do not enter floating point values like -0.666667 OR 2.0.

Question 3 - The matrix A has an LU-decomposition:

Using exact arithmetic determine the unknown elements L₂₁, L₃₁, . . . , U₃₃.

Enter each unknown element as an exact expression.

Question 4 - Which of the following vectors are eigenvectors of

A. x₁ and x₂

B. x₂ only

C. x₁ and x₃

D. x₁ only

Question 5 - If find the eigenvalues of the matrix A.

Your answer should consist of two integers representing the two eigenvalues.

Question 6 - If , then find two eigenvectors of the matrix M.

Your answer should consist of two components for each eigenvectors. These components can be entered as integers or in floating point form. Floating point numbers can be round to 5 decimal digits.

Reference no: EM132402902

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