# Linear algebra: Quiz

Question 1: See, for example, the history of ________.
Gaussian eliminationMatrix (mathematics)Invertible matrixLU decomposition

Question 2: The origin of many of these ideas is discussed in the article on ________.
Linear algebraVector spaceDeterminantMatrix (mathematics)

Question 3: More precisely, the two operations must satisfy a list of axioms chosen to emulate the properties of addition and scalar multiplication of ________ in the coordinate n-space Rn.
Cross productVector spaceEuclidean vectorDot product

Question 4: The method of least squares, first used by ________ in the 1790s, is an early and significant application of the ideas of linear algebra.
Benjamin FranklinJean le Rond d'AlembertIsaac NewtonCarl Friedrich Gauss

Question 5: A fundamental role in linear algebra is played by the notions of ________, span, and linear independence of vectors and basis and the dimension of a vector space.
Linear combinationDual spaceInner product spaceEuclidean vector

Question 6: José Figueroa-O'Farrill, ________
University of OxfordUniversity of CambridgeUniversity of EdinburghUniversity of Bristol

Question 7: If a square matrix has a left inverse or a right inverse then it is invertible (see ________ for other equivalent statements).
Matrix (mathematics)DeterminantLinear algebraInvertible matrix

Question 8: It has extensive applications in the ________ and the social sciences.
Natural scienceMicrobiologyPseudoscienceScientific method

Question 9: there exists an invertible matrix P and a diagonal matrix D such that A = PDP−1) if and only if it has n linearly independent ________.
Vector spaceLinear algebraMatrix (mathematics)Eigenvalue, eigenvector and eigenspace

Question 10: The main structures of linear algebra are vector spaces and ________ between them.
Eigenvalue, eigenvector and eigenspaceLinear mapMatrix (mathematics)Dual space