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21. a. Find a homogeneous linear system of two equations in three unknowns whose solution space consists of those vectors in R that are orthogonal to the vectors a = (1,1,1) and b= (-2,3,0). b. What kind of geometric object is the solution space? c. Find a general solution of the system obtained in part (a). and confirm that Theorem 3.4.3 holds.

21. a. Find a homogeneous linear system of two equations in three unknowns whose solution space consists of those vectors in R that are orthogonal to the vectors a = (1,1,1) and b= (-2,3,0). b. What kind of geometric object is the solution space? c. Find a general solution of the system obtained in part (a). and confirm that Theorem 3.4.3 holds.

Advanced Engineering Mathematics
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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PART (3.4) SECTION 21,22 WRITE ON PAPER PLEASE.
190 CHAPTER 3 Euclidean Vector Spaces 19. x₂ + 5x₂ + x3 + 2x₁ - x = 0 X₁-2x₂-x₂ + 3x + 2x, = 0 20. x₁ + 3x₂ - 4x, = 0 x + 2x + 3x, = 0 21. a. Find a homogeneous linear system of two equations in three unknowns whose solution space consists of those vectors in R that are orthogonal to the vectors a = (1,1,1) and b = (-2,3,0). b. What kind of geometric object is the solution space? c. Find a general solution of the system obtained in part (a). and confirm that Theorem 3.4.3 holds. 22. a. Find a homogeneous linear system of two equations in three unknowns whose solution space consists of those vectors in R³ that are orthogonal to a = (-3, 2, -1) and b=(0, -2,-2). b. What kind of geometric object is the solution space? c. Find a general solution of the system obtained in part (a). and confirm that Theorem 3.4.3 holds. 1 R be an invertible matrix operator on R". Show that the image of a line under multiplication by A is itself a line. 23. a. Let x = x + tv be a line in R" and let T₁: R" b. Let TA: R² R² be multiplication by the matrix - A = Find vector and parametric equations for the image under multiplication by A of the line x = (1,3)+(2, -1). 24. Let TA: R³ → R³ be multiplication by the matrix -4 3 A = Find a vector equation for the image under multiplication by A of the line segment (x, y, z) = (1-1)(2.-3. 1)+(4.1.2) (0 <<1) 20220616_153136.jpg True-False TF. In parts false, at a. The poi line b. The any Working TI. Find t and co row v Theor
Transcribed Image Text:190 CHAPTER 3 Euclidean Vector Spaces 19. x₂ + 5x₂ + x3 + 2x₁ - x = 0 X₁-2x₂-x₂ + 3x + 2x, = 0 20. x₁ + 3x₂ - 4x, = 0 x + 2x + 3x, = 0 21. a. Find a homogeneous linear system of two equations in three unknowns whose solution space consists of those vectors in R that are orthogonal to the vectors a = (1,1,1) and b = (-2,3,0). b. What kind of geometric object is the solution space? c. Find a general solution of the system obtained in part (a). and confirm that Theorem 3.4.3 holds. 22. a. Find a homogeneous linear system of two equations in three unknowns whose solution space consists of those vectors in R³ that are orthogonal to a = (-3, 2, -1) and b=(0, -2,-2). b. What kind of geometric object is the solution space? c. Find a general solution of the system obtained in part (a). and confirm that Theorem 3.4.3 holds. 1 R be an invertible matrix operator on R". Show that the image of a line under multiplication by A is itself a line. 23. a. Let x = x + tv be a line in R" and let T₁: R" b. Let TA: R² R² be multiplication by the matrix - A = Find vector and parametric equations for the image under multiplication by A of the line x = (1,3)+(2, -1). 24. Let TA: R³ → R³ be multiplication by the matrix -4 3 A = Find a vector equation for the image under multiplication by A of the line segment (x, y, z) = (1-1)(2.-3. 1)+(4.1.2) (0 <<1) 20220616_153136.jpg True-False TF. In parts false, at a. The poi line b. The any Working TI. Find t and co row v Theor
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