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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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 2BEXP
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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
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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