MTH603 Quiz 1 by VU Topper RM

following system 2x+2y+z=3x+3y+z=2x+y+z=2 with the initial guess

A. (32,−23,−2) B. (32,57,19)

C. (32,16,13)

D. (32,23,2)

Which of the following system of equation is diagonally dominant?

1. 8x+y−z=5 2x+13y+5z=7 x+2y+9z=3
2. 8x+y−z=5 x+2y+9z=3 2x+13y+5z=7
3. 2x+13y+5z=7 8x+y−z=5 x+2y+9z=3
4. x+2y+9z=3 8x+y−z=5 2x+13y+5z=7

Correct answer: 8x+y−z=5 2x+13y+5z=7 x+2y+9z=3

diagonally dominant coefficient matrix?

1. −2x1+7x2+2x3=56x1−2x2+3x3=1x1+x2−5x3=−13
2. −2x1+7x2+2x3=56x1−2x2+3x3=1x1+x2−5x3=−13
3. 6x1−2x2+3x3=1−2x1+7x2+2x3=5x1+x2−5x3=−13
4. x1+x2−5x3=−136x1−2x2+3x3=1−2x1+7x2+2x3=5

Correct answer: x1+x2−5x3=−136x1−2x2+3x3=1−2x1+7x2+2x3=5

While solving a system of three linear equations in three variables by Jacobi’s method, the first approximate solution is NECESSARY to be taken as (0,0,0). A. True

B. False

system of equation, the following system x+2y+2z=3x+3y+3z=2x+y+5z=2 can be rewritten as A. x=3−2y−2zy=23−x3−zz=25−x5−y5

B. x=32−y−zy=2−x3−zz=25−x5−y5

C. x=1−23y−23zy=1−32x−32zz=1−y2−x2 D. x=3−2y−2zy=2−x−3zz=2−y−x

While solving the system; x+4y = 4, 2x–y = 1 by Gauss-Seidel method, which of the following ordering will lead more rapidly to the desired order of accuracy?

1. 2x-y = 1, x+4y = 4
2. no need to reordering
3. x+4y =1, 2x- y =4
4. x-2y = 1, x+4y =4

Correct answer: x+4y =1, 2x- y =4

In Gauss-Jacobi’s method, the corresponding elements of x(r+1)I replaces those of x(r)I as soon as they become available. A. True

B. False

An augmented matrix may also be used to find the inverse of a matrix by combining it with the …… matrix. A. Inverse B. None of the given choices

C. Identity

D. Square

The system of linear equations; 2x+3y = 6, x+4y = 5 is not strictly diagonal dominant as--------- A. |2| < |3|

B. |2| < |4|

C. |2| < |1| D. |3| < |4|

following system 3x+y+z=112x+5y−z=16x+y+5z=4 with initial guess

A. (113,165,−45) B. (113,−165,−45) C. (113,2615,−725)

D. (113,511,213)

While solving a system of linear equations by Gauss Jordon Method, in which of the following case the partial pivoting is essential?

1. When lower triangular entries are zero
2. When pivots are zero
3. When the upper triangular entries are zero
4. When diagonal entries are zeros
5. 3x+y+z=3x+y+5z=22x+5y−z=4
6. x+y+5z=23x+y+z=32x+5y−z=4
7. 3x+y+z=32x+5y−z=4x+y+5z=2
8. 2x+5y−z=43x+y+z=3x+y+5z=2

In ………… method, matrix [A] of the system of equations is decomposed into the product of two matrices [L] and [U], where [L] is a lower-triangular matrix and [U] is an upper-triangular matrix with 1’s on its main diagonal. A. Gauss-Seidel

B. Crout’s Reduction

C. None of the given choices D. Gaussian elimination

diagonally dominant coefficient matrix?

1. 7x1+5x2−1x3=9−x1+3x2+x3=1x1+2x2+4x3=1
2. 4x1+2x2+3x3=17x1+5x2−8x3=9−5x1+3x2+2x3=1
3. 4x1+2x2+3x3=1−5x1+3x2+2x3=17x1+5x2−8x3=9
4. −5x1+3x2+2x3=17x1+5x2−8x3=94x1+2x2+3x3=1

Correct answer: 4x1+2x2+3x3=17x1+5x2−8x3=9−5x1+3x2+2x3=1