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M 340 L Unique number 53280 QUIZ # 3 LAST NAME (PRINT) ………………………………. First Name ………………….. TRUE FALSE 1) If A and B are nxn matrices, with detA=2 and detB=3, then det (A+B) = 5. ……………………F…. 2) det AtA > 0 or = 0 ……T…………………… 3) If A3 = 0, then det A = 0. ..……T…………………… 4) The null space of A is the solution set of A x = 0 . …..T………………… 5) The column space of A is the range of the mapping x Ax. ……T………………… 6) The range of a linear transformation is a vector space. ..…T…………………. 7) Col A is the set of all solutions of the equation Ax = b. ……………………F… 8) The column space of a mxn matrix is Rm. ……………………F…. 9) If a finite set S of non zero vectors spans a vector space V then some subset of S is a basis for V. 10) If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col A. 11) If dim V = p, then there exists a spanning set of p+1 vectors in V. 12) If p > or = 2 and dim V = p, then every set of p-1 non Zero vectors is linearly independent. 13) The dimension of the null space of A is the number of columns of A that are not pivot columns. ….T...………………… …………………F… …T………………… ……………………F… …T…………………… M 340 L Unique number 53280 Up to Date PRACTICE QUIZ # 3 LAST NAME (PRINT) ………………………………. First Name ………………….. TRUE 1) det (A+B) = det A + det B FALSE .………………………. 2) If A is invertible (det A )(det A-1 ) = 1. ………………………… 3) det At = - det A. .……………………… 4) A null space is a vector space. …..………………… 5) Nul A is the Kernel of the mapping x Ax. ……………………… 6) The range of a linear transformation is a vector space. ..……………………. 7) Col A is the set of all vectors that can be written as Ax for some x. ……………………… 8) The Null space of a mxn matrix is Rm. ………………………. 9) A basis is a linearly independent set which is as large as possible. …....………………… 10) If B is any echelon form of a matrix A, then the pivot columns of B form a basis for the column space of A. …..…………………… 11) If B is any echelon form of a matrix A, then A and B have the same null space. …………………………. 12) If B is obtained from a matrix A by several elementary row operations, then rank B = rank A. ………………………… 13) The pivot columns of A provide a basis of Col A. …………………………