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MTH603 Numerical Analysis Quiz No 1 Solution and Discussion Spring 2014 Due Date: May 19, 2014

MTH603 Numerical Analysis  Quiz No 1 Solution and Discussion Spring 2014 Due Date: May 19, 2014

Quiz No.01 will open on May 15, 2014 and the last date of taking quiz is May 19, 2014

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Quiz #1.

  1. In __________ method, a system is reduced to an equivalent diagonal form using elementary transformations.
    1. Jacobi’s
    2. Gauss seidel
    3. relaxation
    4. Gaussian elimination.
    5. The linear equation: 2X + 0Y – 2 = 0 has ________ solution/ solutions.
      1. Unique
      2. No solution
      3. Infinite many
      4. Finite many
      5. Relaxation method is a/an __________
        1. Direct method
        2. Iterative method
        3. If the determinant of a matrix A is not equal to zero then the system of equation will have ____.
          1. A unique solution
          2. Many solution
          3. Infinite many solution
          4. None of the given choice
          5. In ________ method the elements sbove and below the diagonal are simultaneously made zero.
            1. Jacobi’s
            2. Gauss seidel
            3. Gauss Jordon elimination
            4. Relaxation
            5. Gauss seidel method is also known as method of __________
              1. Successive displacement
              2. Iterations
              3. False position
              4. None of the above given choice
              5. While solving a system of linear equations by gauss Jordon metod, after all the elementary row operations if there lefts also zeros on the main diagonal then which of the is true about the system?
                1. System may have unique solutions
                2. System has no solution
                3. System may have multiple numbers of finite solutions
                4. System may have infinite many solutions.
                5. If the product of two matrices is an identity matrices that is AB = 1, then which of the following is true?
                  1. A is transpose of B
                  2. A is inverse of B
                  3. A is Singular
                  4. B is singular
                  5. The system of linear equation: 2X + 3Y 6, X + 4 = 5 is not strictly diagonal dominant as ______
                    1. Sparse matrix is a matrix with _____
                      1. Some elements are zero
                      2. Many elements are zero
                      3. Some elements are one
                      4. Many elements are one

Quez # 2.

  1. The linear equation: 0X + 0y = 2 has _________ solution/ solutions.
    1. Unique
    2. No solution
    3. Infinite many
    4. finite many
    5. Gauss elimination and gauss Jordan methods are popular among many methods for finding the ___ of a matrix.
      1. Identity
      2. Transpose
      3. Inverse
      4. None of the given choices
      5. While using relaxation method, which of the following is increment “dxi” corresponding to the largest residual for 1at iteration on the system: 2X + 3Y = 1, 3X + 2Y =-4?
        1. -2
        2. 2
        3. 3
        4. 4
        5. While using relaxation method which of the following is the largest residual for 1st iteration on the system 3X + 3Y = 1, 3X * 2Y = -4?
          1. -4
          2. 3
          3. 2
          4. 1
          5. While using relaxation method which of the following is the largest residual for 1st iteration on the system 3X + 3Y = 1, 3X * 2Y = -4?
            1. [2,3]
            2. [3,-2]
            3. [-2,3]
            4. [1,4]
            5. Which of the following rearrangement make strictly diagonal dominant the system of linear equation; X – 3Y = -2, -6X + 4Y +11Z = 1, 5X – 2Y – 2Z = 9?
              1. 5X – 2Y – 2Z = 9, X – 3Y = -2, -6X + 4Y +11Z = 1
              2. -6X + 4Y +11Z = 1, X – 3Y = -2, 5X – 2Y – 2Z = 9
              3. 5X – 2Y – 2Z = 9, X – 3Y = -2, -6X + 4Y +11Z = 1
              4. No need to rearrange as system is already in diagonal dominant form.
              5. Back substitution procedure is used in ______.
                1. Gaussian elimination method
                2. Jacobi’s method
                3. Gauss-seidel method
                4. None of the given choice.
                5. By using determinants we can easily check that the solution of the given system of linear equation exits and it is unique.
                  1. True
                  2. False
                  3. The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
                    1. True
                    2. False
                    3. A and its transpose matrix have _______ eigenvalues.
                      1. Same
                      2. Differnts

Quiz # 3.

  1. The absolute value of a determinant (|detA|) is the product of the absolute values of the eigenvalues of matrix A
    1. True
    2. False
    3. Central Difference method is the finite difference method
      1. True
      2. False
      3. For a function; y=f(x), if y0, y1 and y2 are 2,3 and 5 respectively then which of the following will be 2nd order Leading difference at y0 = 2 ?
        1. 1
        2. -1
        3. 2
        4. -2
        5. For differences methods we require the set of values.
          1. True
          2. False
          3. Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.
            1. True
            2. False
            3. Eigenvalues of a symmetric matrix are all _________.
              1. Real
              2. Zero
              3. Positive
              4. An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.
                1. Real
                2. Zero
                3. Positive
                4. d.      True
                5. The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric ________ definite matrices A.
                  1. a.      Positive
                  2. Negative
                  3. Differences methods find the ________ solution of the system. 
                    1. a.      numerical
                    2. Analytical
                    3. The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power. 
                      1. (x-1)^3
                      2. (x+1)^3          i m not sure about this answer
                      3. x^3-1
                      4. x^3+1
                      5. The Power method can be used only to find the eigen value of A that is largest in absolute value—----------we call this eigen value the dominant eigen value of A.
                        1. TRUE
                        2. b.      FALSE
                        3. The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.
                          1. main diagonal
                          2. last column
                          3. last row
                          4. first row     i m not sure about this answer
                          5. If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A. 
                            1. TRUE
                            2. b.      FALSE
                            3. A 3 x 3 identity matrix have three and different eigen values.
                              1. TRUE
                              2. FALSE

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