MTH 212 Questions & Answers

Question: Given that U and V are vector spaces over a field F LetT  Urightarrow V be a linear transformation then the set xin UTx  0 is called the

Answer:C: kernel of T

Question: beginbmatrix0 13 12535 4endbmatrix is a matrix Answer:A: symmetric Question: The dimension of the matrix beginbmatrix12532810 5 210endbmatrix is Answer:B: 3 by 4 Question: A square matrix whose tranpose is equal to the negative of the matrix itself is known as Answer:A: skew symmetric Question: A one one and onto linear transformation is Answer:C: invertible Question: The determinant of beginbmatrixx21x52x3x4endbmatrix is Answer:A: 2x3 x2 24x15
Question: The transpose ofbeginbmatrix1 1542637 2endbmatrix is a matrix Answer:B: beginbmatrix143 12756 2endbmatrix Question: The order of the matrix beginbmatrix125ba3281C0 5 2 510abcdendbmatrix is Answer:B: 5 by 4 Question: The determinant of beginbmatrix143 12756 2endbmatrix is Answer:A: 38 Question: The size of the matrix beginbmatrix12281 510endbmatrix is Answer:A: 2 by 4 Question: A matrix whose determinant is zero is called Answer:C: singular Question: The dimension of the kernel of T is the same as the of T Answer:C: nullity Question: The determinant of beginbmatrix231000459endbmatrix is Answer:C: zero Question: For any linear transformation T Urightarrow V let the dimension of U be finite then Ker T has a dimension Answer:A: finite Question: Every vector space is isomorphic to its dual Answer:B: 2nd
Question: Let T in AV then T is invertible if and only if the constant term in the minimal polynomial of T is Answer:A: not zero Question: The of a row reduced echelon matrix is equal to the number of its non zero rows Answer:B: rank Question: Every matrix can be reduced to a row reduced echelon matrix by a of elementary row operations Answer:A: finite sequence Question: The determinant rank of an m x n matrix A is equal to the of A Answer:B: rank Question: The determinant of beginbmatrix2x x 12x3x1 12endbmatrix is Answer:C: 7x25x2 Question: Let T Urightarrow V be a linear transformation then rank T nullity T Answer:C: dim U Question: What is the determinant rank of the determinant ofbeginbmatrix142536endbmatrix Answer:C: 2 Question: One of the following is not a property of determinants Answer:B: If two rows or columns are interchanged the determinant is zero Question: The determinant of beginbmatrix1 2 15x2x3 x2endbmatrix is Answer:B: 2x2 2x20
Question: Let L R3rightarrow R be the map given by Lxyz x y z What is nullity L Answer:C: 2 Question: T is called if for each v in V there exist u in U such that Tu v Answer:A: surjective Question: If U be a vector space over FThen the space LUF is called the of U Answer:dual space Question: The of T is defined to be the dimension of Kernel of T Answer:Nullity Question: Every vector space is isomorphic to its dual Answer:second Question: A matrix with only row is called a row matrix or row vector Answer:one Question: If X and Y are matrices and XYYXI Then X is said to be Answer:Non singular Question: The of a matrix is equal to the number of pivots in an echelon form of A Answer:rank Question: The dimension of R of T is called of T Answer:rank Question: A matrix that does not have inverse is called aan matrix Answer:singular Question: Suppose A m by nmatrix the m horizontal list of scalars are called Answer:rows Question: A rectangular array of scalars within square brackets is square is called Answer:matrix Question: If X and Y are matrices and XY YX I Y is said to be the of A Answer:inverse
Question: A square matrix A is said to be invertible if there exists a matrix B such that Answer:ABBAI Question: A matrix obtained by subjecting Ito an elementary row or column operation is called aan Answer:elementary Question: The matrix 0 is called Answer:zero Question: The number appearing in the various positions of a matrix are called the of the matrix Answer:elements Question: The pair of numbers and is called the of the matrix Answer:Size Question: An matrix is said to be of order n Answer:mn Question: A is a matrix with the same number of rows and columns Answer:square Question: A matrix with only one column is called a vector Answer:Column Question: A and B are two matrices and ABBA Then A and Bare said to be Answer:Commutative

No comments