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MTH 212 Questions & Answers

1 0 105 - MTH 212 Questions & Answers
1 0 105 - 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

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