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```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 theAnswer:C: kernel of TQuestion: beginbmatrix0 13 12535 4endbmatrix is a  matrixAnswer:A: symmetricQuestion: The dimension of the matrix beginbmatrix12532810 5 210endbmatrix isAnswer:B: 3 by 4Question: A square matrix whose tranpose is equal to the negative of the matrix itself is known asAnswer:A: skew symmetricQuestion: A one one and onto linear transformation is Answer:C: invertibleQuestion: The determinant of beginbmatrixx21x52x3x4endbmatrix is Answer:A:  2x3  x2  24x15Question: The transpose ofbeginbmatrix1 1542637 2endbmatrix is a  matrixAnswer:B: beginbmatrix143 12756 2endbmatrixQuestion: The order of the matrix beginbmatrix125ba3281C0 5 2 510abcdendbmatrix isAnswer:B: 5 by 4Question: The determinant of beginbmatrix143 12756 2endbmatrix is Answer:A: 38Question: The size of the matrix beginbmatrix12281 510endbmatrix isAnswer:A: 2 by 4Question: A matrix whose determinant is zero is called  Answer:C: singularQuestion: The dimension of the kernel of T is the same as the  of TAnswer:C: nullityQuestion: The determinant of beginbmatrix231000459endbmatrix isAnswer:C: zeroQuestion: For any linear transformation T  Urightarrow V  let the dimension of U be finite then Ker T has a  dimensionAnswer:A: finiteQuestion: Every vector space is isomorphic to its dualAnswer:B: 2ndQuestion: 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 zeroQuestion: The  of a row reduced echelon matrix is equal to the number of its non zero rowsAnswer:B: rankQuestion: Every matrix can be reduced to a row reduced echelon matrix by a  of elementary row operationsAnswer:A: finite sequenceQuestion: The determinant rank of an m x n matrix A is equal to the  of AAnswer:B: rankQuestion: The determinant of beginbmatrix2x x 12x3x1 12endbmatrix is Answer:C: 7x25x2Question: Let  T  Urightarrow V be a linear transformation then rank T  nullity T  Answer:C: dim UQuestion: What is the determinant rank of the determinant ofbeginbmatrix142536endbmatrixAnswer:C: 2Question: One of the following is not a property of determinantsAnswer:B: If two rows or columns are interchanged the determinant is zeroQuestion: The determinant of beginbmatrix1 2 15x2x3 x2endbmatrix is Answer:B: 2x2 2x20Question: Let L R3rightarrow R be the map given by Lxyz  x  y  z What is nullity LAnswer:C: 2Question: T is called  if for each v in V there exist u in U such that Tu  vAnswer:A: surjectiveQuestion: If U be a vector space over FThen the space LUF is called the  of UAnswer:dual spaceQuestion: The  of  T is defined to be the dimension of  Kernel of TAnswer:NullityQuestion: Every vector space is isomorphic to its  dualAnswer:secondQuestion: A matrix with only  row is called a row matrix or row vectorAnswer:oneQuestion: If X and Y are matrices and XYYXI Then X is said to beAnswer:Non singularQuestion: The  of a matrix is equal to the number of pivots in an echelon form of AAnswer:rankQuestion: The dimension of R of T is called  of TAnswer:rankQuestion: A matrix that does not have inverse is called aan  matrixAnswer:singularQuestion: Suppose A m by nmatrix the m horizontal list of scalars are called Answer:rowsQuestion: A rectangular array of scalars within square brackets is square is calledAnswer:matrixQuestion: If X and Y are matrices and XY YX  I Y is said to be the  of AAnswer:inverseQuestion: A square matrix A is said to be invertible if there exists a matrix B such thatAnswer:ABBAIQuestion: A matrix obtained by subjecting  Ito an elementary row or column operation is called aan Answer:elementaryQuestion: The matrix 0 is called Answer:zeroQuestion: The number appearing in the various positions of a matrix are called the  of the matrixAnswer:elementsQuestion: The pair of numbers and is called the   of the matrixAnswer:SizeQuestion: An  matrix is said to be of order nAnswer:mnQuestion: A  is a matrix with the same number of rows and columnsAnswer:squareQuestion: A matrix with only one column is called a  vectorAnswer:ColumnQuestion: A and B are two matrices and ABBA Then A and Bare said to be Answer:Commutative