1. Solve the system of linear equation. x+ y+ 3z = 2 3x – 2y + 2z = -2 3x + 2y + 8z = 6

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. Solve the system of linear equation.
x+ y+ 3z = 2
3x – 2y + 2z = -2
3x + 2y + 8z = 6
2. Find solution set of the system by Gauss-Jordan elimination
X1- X2 + 5x3 + 4x4 = 1
3x1- 4x, + x3 – x4 = 3
(4x1- 5x2 + 6x3 + 3x4 = 4
3. Is thefollowing set of vectors in P, is linear independent? Prove the answer.
{1+ 3x + 3x?; 1 – 2x + 2x?; 3+ 2x + 8x²}
4. Find representation of the vector v = 2 – 2x + 6x² with respect to following basis.
{1+3x + 3x?; 1 – 2x + 2x?;3+ 2x+ 8x²}
5. Find a basis for the row space of the following matrix.
1.
-2
5
4
3 -4 1
-1
4 -5
6 3
Transcribed Image Text:1. Solve the system of linear equation. x+ y+ 3z = 2 3x – 2y + 2z = -2 3x + 2y + 8z = 6 2. Find solution set of the system by Gauss-Jordan elimination X1- X2 + 5x3 + 4x4 = 1 3x1- 4x, + x3 – x4 = 3 (4x1- 5x2 + 6x3 + 3x4 = 4 3. Is thefollowing set of vectors in P, is linear independent? Prove the answer. {1+ 3x + 3x?; 1 – 2x + 2x?; 3+ 2x + 8x²} 4. Find representation of the vector v = 2 – 2x + 6x² with respect to following basis. {1+3x + 3x?; 1 – 2x + 2x?;3+ 2x+ 8x²} 5. Find a basis for the row space of the following matrix. 1. -2 5 4 3 -4 1 -1 4 -5 6 3
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