3 Questions
Koja je formula korištena za pronalaženje matrice ortogonalne projekcije P na stupčani prostor matrice A u Problemu 1?
Formula iz LADW-a
Koji je cilj Problema 2?
Pronaći linearnu jednadžbu koja najbolje odgovara skupu podataka korištenjem najmanjih kvadrata
Što je potrebno da bi se tvrdilo da je A*A invertibilna u Problemu 4?
A*A mora imati rang n
Study Notes
- The text provides four problems related to linear algebra.
- Problem 1 involves finding the matrix of the orthogonal projection P onto the column space of a given matrix A.
- The projection matrix P is found using a formula from LADW.
- The size of P is not necessarily 3x2 even though the column space of A has dimension 2.
- The geometric meaning of |X - Px| is not specified.
- Problem 2 involves finding the linear equation that best fits a given set of data using least squares.
- Problem 3 involves finding the quadratic equation that best fits a given set of data using least squares.
- Problem 4 involves showing that ker(A) = ker(A*A).
- Ker(A) = ker(AA) implies that AA is invertible if and only if A has rank n.
- The invertibility of AA is important for solving the normal equation AAx - A*b.
Test your knowledge of linear algebra with this quiz! From finding orthogonal projections and least squares equations to demonstrating the relationship between kernel and rank, this quiz covers a range of important concepts. Sharpen your skills and see how much you know about linear algebra.
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