Скачать или смотреть Delhi University (DU) | MSc Mathematics Entrance-2014 Solutions | Linear Algebra Soutions |

Delhi University (DU) | MSc Mathematics Entrance-2014 | Linear Algebra Soutions |
In this video we have discussed solutions of following problems:
(1)Which one of the following is true for the transformation T : M n → C defined by
T(A) = tr(A) ? A) Nullity of T is n^2 − 1 B) T is one-to-one C) Rank of T is n D) T (AB) = T (A)T (B) for all A, B ∈ M n×n
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(2)Which one of the following is true for the transformation
T : P 2 (R) → P 2 (R) defined by T (f ) = f + f 0 + f 00 ?
A)T is one-to-one but not onto
B)T is onto but not one-to-one
C)T is invertible
D)the matrix of T with respect to the basis {1, x, x^2 } is upper triangular.
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(3)Let W 1 = {A ∈ M n (C) : A ij = 0 ∀ i ≤ j} and W 2 is the set of symmetric matrices
of order n. Then the dimension of W 1 + W 2 is
A) n B) 2n C) n^2 D) n^2 − n.
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#Nullity #Tisonetoone #RankofT #T(AB)=T (A)T(B) #symmetricmatrices