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Test Your Linear Algebra Skills

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Questions and Answers

Koja je formula korištena za pronalaženje matrice ortogonalne projekcije P na stupčani prostor matrice A u Problemu 1?

Formula za skalarni produkt

Formula iz LADW-a (correct)

Formula za vektorski produkt

Formula za determinantu

Koji je cilj Problema 2?

Pronaći linearnu jednadžbu koja najbolje odgovara skupu podataka korištenjem najmanjih kvadrata (correct)

Pronaći matricu ortogonalne projekcije

Pronaći kvadratnu jednadžbu koja najbolje odgovara skupu podataka korištenjem najmanjih kvadrata

Pokazati da je ker(A) = ker(A*A

Što je potrebno da bi se tvrdilo da je A*A invertibilna u Problemu 4?

A*A mora imati rang manji od n

A*A mora imati rang n (correct)

Ker(A) mora biti suprotno proporcionalan Ker(A*A

Ker(A) mora biti jednak Ker(A*A

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.

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Description

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.