Consider a system of equations where the ith equation is ai i=bi i+1+ci i-1+di. While solving this system using Thomas algorithm, we get i=Pi i+1+Qi. What are P1 and Q1?

(P_1= frac{d_1}{a_1-c_1};Q_1= frac{b_1}{a_1-c_1} )

(P_1= frac{b_1}{a_1-c_1};Q_1= frac{d_1}{a_1-c_1} )

(P_1= frac{d_1}{a_1};Q_1= frac{b_1}{a_1} )

(P_1= frac{b_1}{a_1};Q_1= frac{d_1}{a_1} )

Consider a system of equations where the ith equation is ai i=bi (i+1)+ci (i+1)+di. While solving this system using Thomas algorithm, we get i=Pi (i+1)+Qi. What are Pi and Qi?

(P_i= frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}};Q_i= frac{d_i}{a_i-c_i P_{i-1}} )

(P_i= frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}};Q_i= frac{b_i}{a_i-c_i P_{i-1}} )

(P_i= frac{b_i}{a_i-c_i P_{i-1}};Q_i= frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}} )

(P_i= frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}};Q_i= frac{d_i}{a_i-c_i P_{i-1}} )

(P_i= frac{d_i}{a_i-c_i P_{i-1}};Q_i= frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}} )

Explore topic-wise MCQs in Computational Fluid Dynamics.

This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Computational Fluid Dynamics knowledge and support exam preparation. Choose a topic below to get started.

1.	Consider a system of equations where the i^th equation is a_i _i=b_i _i+1+c_i _i-1+d_i. While solving this system using Thomas algorithm, we get _i=P_i _i+1+Q_i. What are P₁ and Q₁?
A.	(P_1= frac{d_1}{a_1-c_1};Q_1= frac{b_1}{a_1-c_1} )
B.	(P_1= frac{b_1}{a_1-c_1};Q_1= frac{d_1}{a_1-c_1} )
C.	(P_1= frac{d_1}{a_1};Q_1= frac{b_1}{a_1} )
D.	(P_1= frac{b_1}{a_1};Q_1= frac{d_1}{a_1} )
Answer» E.

Discussion

2.	After finding all the values of P_i and Q_i, in which order are the values of _i found?
A.	Forward
B.	Simultaneously
C.	Backwards
D.	Depends on the problem
Answer» D. Depends on the problem

Discussion

3.	While solving a system of equations with the Thomas algorithm, in which order are the values of P_i and Q_i found?
A.	Backwards
B.	Forward
C.	Simultaneously
D.	Depends on the problem
Answer» C. Simultaneously

Discussion

4.	Using the Thomas algorithm, if the i^th unknown is _i=P_i _i+1+Q_i. what is the last unknown value _N equal to?
A.	0
B.	P<sub>N</sub>
C.	Q<sub>N</sub>
D.	1
Answer» D. 1

Discussion

5.	Let the i^th equation of a system of n equations be a_i _i=b_i _i+1+c_i _i-1+d_i. Which of these is correct?
A.	c<sub>N</sub>=0; b<sub>N</sub>=0
B.	c<sub>N</sub>=0; b<sub>1</sub>=0
C.	c<sub>1</sub>=0; b<sub>N</sub>=0
D.	c<sub>1</sub>=0; b<sub>1</sub>=0
Answer» D. c<sub>1</sub>=0; b<sub>1</sub>=0

Discussion

6.	Consider a system of equations where the i^th equation is a_i _i=b_i _(i+1)+c_i _(i+1)+d_i. While solving this system using Thomas algorithm, we get _i=P_i _(i+1)+Q_i. What are P_i and Q_i?
A.	(P_i= frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}};Q_i= frac{b_i}{a_i-c_i P_{i-1}} )
B.	(P_i= frac{b_i}{a_i-c_i P_{i-1}};Q_i= frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}} )
C.	(P_i= frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}};Q_i= frac{d_i}{a_i-c_i P_{i-1}} )
D.	(P_i= frac{d_i}{a_i-c_i P_{i-1}};Q_i= frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}} )
Answer» C. (P_i= frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}};Q_i= frac{d_i}{a_i-c_i P_{i-1}} )

Discussion

7.	Thomas algorithm is _________
A.	an analytical method
B.	a direct method
C.	an iterative method
D.	a least squares method
Answer» D. a least squares method

Discussion

8.	Thomas algorithm can be used to solve __________
A.	any matrix
B.	all square matrices
C.	only penta-diagonal matrices
D.	only tri-diagonal matrices
Answer» E.

Discussion

9.	Thomas algorithm is a ___________
A.	Linear equations solver
B.	Quadratic equations solver
C.	Discretization method
D.	Linear least square system
Answer» B. Quadratic equations solver

Discussion

Explore topic-wise MCQs in Computational Fluid Dynamics.

Consider a system of equations where the ith equation is ai i=bi i+1+ci i-1+di. While solving this system using Thomas algorithm, we get i=Pi i+1+Qi. What are P1 and Q1?

After finding all the values of Pi and Qi, in which order are the values of i found?

While solving a system of equations with the Thomas algorithm, in which order are the values of Pi and Qi found?

Using the Thomas algorithm, if the ith unknown is i=Pi i+1+Qi. what is the last unknown value N equal to?

Let the ith equation of a system of n equations be ai i=bi i+1+ci i-1+di. Which of these is correct?

Consider a system of equations where the ith equation is ai i=bi (i+1)+ci (i+1)+di. While solving this system using Thomas algorithm, we get i=Pi (i+1)+Qi. What are Pi and Qi?

Thomas algorithm is _________

Thomas algorithm can be used to solve __________

Thomas algorithm is a ___________

Consider a system of equations where the i^th equation is a_i _i=b_i _i+1+c_i _i-1+d_i. While solving this system using Thomas algorithm, we get _i=P_i _i+1+Q_i. What are P₁ and Q₁?

After finding all the values of P_i and Q_i, in which order are the values of _i found?

While solving a system of equations with the Thomas algorithm, in which order are the values of P_i and Q_i found?

Using the Thomas algorithm, if the i^th unknown is _i=P_i _i+1+Q_i. what is the last unknown value _N equal to?

Let the i^th equation of a system of n equations be a_i _i=b_i _i+1+c_i _i-1+d_i. Which of these is correct?

Consider a system of equations where the i^th equation is a_i _i=b_i _(i+1)+c_i _(i+1)+d_i. While solving this system using Thomas algorithm, we get _i=P_i _(i+1)+Q_i. What are P_i and Q_i?