cos cos Problem 1: Find the matrix which sends the standard basis €₁, €2 € R² to the vectors v0,1 = ,V0,2 = sin matrix which rotates plane by 0. Test this matrix out by picking a few different values and seeing what happens. Next try to figure out how to use these ideas to rotate the "ry" plane in R³ by 0, then the "az" plane in R³ by p. Compose these two matrices and try them out with a few choices of values for and p. Finally, if you take any of our matrices and perform AT A, do you get anything interesting? sin 0 0 (9).. (1) 1 ,V2 = following multiplications are defined: v₁v2, vf -v2, 0₁-05, or of v? Which one of these is equal to the inner product? Note that the remaining one is called the "outerproduct". In reality we should have defined the inner product as: (v₁,v2): vf · v₂. Problem 2: Consider the two vectors, v₁ = . Think of these both as 3 x 1 matrices. Which of the

cos cos Problem 1: Find the matrix which sends the standard basis €₁, €2 € R² to the vectors v0,1 = ,V0,2 = sin matrix which rotates plane by 0. Test this matrix out by picking a few different values and seeing what happens. Next try to figure out how to use these ideas to rotate the "ry" plane in R³ by 0, then the "az" plane in R³ by p. Compose these two matrices and try them out with a few choices of values for and p. Finally, if you take any of our matrices and perform AT A, do you get anything interesting? sin 0 0 (9).. (1) 1 ,V2 = following multiplications are defined: v₁v2, vf -v2, 0₁-05, or of v? Which one of these is equal to the inner product? Note that the remaining one is called the "outerproduct". In reality we should have defined the inner product as: (v₁,v2): vf · v₂. Problem 2: Consider the two vectors, v₁ = . Think of these both as 3 x 1 matrices. Which of the

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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