Question 1. Solve the following system of linear equations using gaussian elimination. 2x + 4y + 2z = 10 2x + y +z =6 + y = 3
Question 1. Solve the following system of linear equations using gaussian elimination. 2x + 4y + 2z = 10 2x + y +z =6 + y = 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Question 1.
Solve the following system of linear equations using gaussian elimination.
2x + 4y + 2z = 10
2х
+ y +z = 6
+ y
= 3
Question 2.
A. Using the key matrix A = . Encode the message: sohar college
(Note: Use 0 for space)
B. If possible, find the inverse of the matrix A=
l2
Question 3.
Let the functions f, g and h be defined as follows:
f:R-R, f(x)=x²+3
g: R-R, g(x)= 5x+5
h: R-R, h(x) = 3x-2
Find
g• (f o h)
gl
Prove that g(x) is one-one correspondane.
(a)
(b)
(c)
Question 4.
A. If the 4th term of a geometric progression is 24 and the 6th term is 96, then find the 8th term of this GP.
B. For the following function from (a, b, c, d, e} to (1, 2,3, 4,5}, decide whether it is one-one
correspondence or not. Explain your answer.
R = {(a, 1), (d, 3), (b, 2), (c, 1), (e,3)}
Question 5.
A. Use Karnaugh map to reduce the Boolean expression:
F-A'BC + AВС+ А'ВС" + АВС + АВС
B. Draw the digital circuits for both the original and simplified expressions.
1
Question 6.
A. Use laws of Boolean algebra to simplify the following Boolean expression
[(X'Y) +X']'
Page 1 of 2
B. Convert the following truth table into Boolean expression
X Y Z _G
0 001
1
1
1
1-
1
1
1
1
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facb09391-5ac7-452b-8339-2c5941cb668f%2Ffc5eace0-f183-4766-8747-06f4bab7dbcf%2Fir097cd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 1.
Solve the following system of linear equations using gaussian elimination.
2x + 4y + 2z = 10
2х
+ y +z = 6
+ y
= 3
Question 2.
A. Using the key matrix A = . Encode the message: sohar college
(Note: Use 0 for space)
B. If possible, find the inverse of the matrix A=
l2
Question 3.
Let the functions f, g and h be defined as follows:
f:R-R, f(x)=x²+3
g: R-R, g(x)= 5x+5
h: R-R, h(x) = 3x-2
Find
g• (f o h)
gl
Prove that g(x) is one-one correspondane.
(a)
(b)
(c)
Question 4.
A. If the 4th term of a geometric progression is 24 and the 6th term is 96, then find the 8th term of this GP.
B. For the following function from (a, b, c, d, e} to (1, 2,3, 4,5}, decide whether it is one-one
correspondence or not. Explain your answer.
R = {(a, 1), (d, 3), (b, 2), (c, 1), (e,3)}
Question 5.
A. Use Karnaugh map to reduce the Boolean expression:
F-A'BC + AВС+ А'ВС" + АВС + АВС
B. Draw the digital circuits for both the original and simplified expressions.
1
Question 6.
A. Use laws of Boolean algebra to simplify the following Boolean expression
[(X'Y) +X']'
Page 1 of 2
B. Convert the following truth table into Boolean expression
X Y Z _G
0 001
1
1
1
1-
1
1
1
1
1
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