A = I1 = -1 2 0 2 Verify the the following are eigenvectors and find their corresponding eigenvalues: (0) : R³ R³ x2 = (1) --- () 0 = 1 cos - sin 0 Problem 2: Consider the matrix Ro= Now choose 0 = π/3 and solve for the the eigenvalues and try to solve for eigenvectors. sin 0 cos for the scalar variable 0. Find the characteristic polynomial.
A = I1 = -1 2 0 2 Verify the the following are eigenvectors and find their corresponding eigenvalues: (0) : R³ R³ x2 = (1) --- () 0 = 1 cos - sin 0 Problem 2: Consider the matrix Ro= Now choose 0 = π/3 and solve for the the eigenvalues and try to solve for eigenvectors. sin 0 cos for the scalar variable 0. Find the characteristic polynomial.
A = I1 = -1 2 0 2 Verify the the following are eigenvectors and find their corresponding eigenvalues: (0) : R³ R³ x2 = (1) --- () 0 = 1 cos - sin 0 Problem 2: Consider the matrix Ro= Now choose 0 = π/3 and solve for the the eigenvalues and try to solve for eigenvectors. sin 0 cos for the scalar variable 0. Find the characteristic polynomial.
Transcribed Image Text:Problem 1: Consider the matrix,
A =
I1 =
1
-1
0
-1 0
2 1
-1
1
: R³ R³
Verify the the following are eigenvectors and find their corresponding eigenvalues:
1
(1) · --- (-:-). ²- (²-3)
x2 =
I3 =
cos
- sin 0
Problem 2: Consider the matrix Re
sin 0
Now choose 0 = π/3 and solve for the the eigenvalues and try to solve for eigenvectors.
Cos
for the scalar variable 0. Find the characteristic polynomial.
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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