# MTH 212 Questions & Answers

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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 the
Answer:C: kernel of T
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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

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