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Which one of the following is true?
  • a)
    There are infinitely many one to one linear transformation from R4 to R3
  • b)
    The dimension of the vector space of all 3 x 3 skew-symmetric matrices over the field of real no. is 6.
  • c)
    Let F be a field and A be a fixed n x n matrix over F.   a linear transformation such  that T(B)= AB for  then the characteristic polynomial for A is the same as the characteristic polynomial for T.
  • d)
    A two-dimensional vector space over a field with 2 elements has exactly 3 different basis.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which one of the following is true?a)There are infinitely many one to ...
If T : R4 → R3, be a L.T. then this map cannot be one-one, since dim (R4) = 4.
So ker (T) ≠ {0}.
(B) We know if V be a V.S. of all (n x n) skew-symmetric matrices then

In this case we cannot find out matrix representation of T w.r. to basis  of Mn(Q) but if F =R1, Then always char. eqn of T is same as A.
⇒ only (D) is correct.
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Most Upvoted Answer
Which one of the following is true?a)There are infinitely many one to ...
If T : R4 → R3, be a L.T. then this map cannot be one-one, since dim (R4) = 4.
So ker (T) ≠ {0}.
(B) We know if V be a V.S. of all (n x n) skew-symmetric matrices then

In this case we cannot find out matrix representation of T w.r. to basis  of Mn(Q) but if F =R1, Then always char. eqn of T is same as A.
⇒ only (D) is correct.
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Community Answer
Which one of the following is true?a)There are infinitely many one to ...
If T : R4 → R3, be a L.T. then this map cannot be one-one, since dim (R4) = 4.
So ker (T) ≠ {0}.
(B) We know if V be a V.S. of all (n x n) skew-symmetric matrices then

In this case we cannot find out matrix representation of T w.r. to basis  of Mn(Q) but if F =R1, Then always char. eqn of T is same as A.
⇒ only (D) is correct.
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Which one of the following is true?a)There are infinitely many one to one linear transformation from R4 to R3b)The dimension of the vector space of all 3 x 3 skew-symmetric matrices over the field of real no. is 6.c)Let F be a field and A be a fixed n x n matrix over F.a linear transformation such that T(B)= AB forthen the characteristic polynomial for A is the same as the characteristic polynomial for T.d)A two-dimensional vector space over a field with 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer?
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Which one of the following is true?a)There are infinitely many one to one linear transformation from R4 to R3b)The dimension of the vector space of all 3 x 3 skew-symmetric matrices over the field of real no. is 6.c)Let F be a field and A be a fixed n x n matrix over F.a linear transformation such that T(B)= AB forthen the characteristic polynomial for A is the same as the characteristic polynomial for T.d)A two-dimensional vector space over a field with 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which one of the following is true?a)There are infinitely many one to one linear transformation from R4 to R3b)The dimension of the vector space of all 3 x 3 skew-symmetric matrices over the field of real no. is 6.c)Let F be a field and A be a fixed n x n matrix over F.a linear transformation such that T(B)= AB forthen the characteristic polynomial for A is the same as the characteristic polynomial for T.d)A two-dimensional vector space over a field with 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is true?a)There are infinitely many one to one linear transformation from R4 to R3b)The dimension of the vector space of all 3 x 3 skew-symmetric matrices over the field of real no. is 6.c)Let F be a field and A be a fixed n x n matrix over F.a linear transformation such that T(B)= AB forthen the characteristic polynomial for A is the same as the characteristic polynomial for T.d)A two-dimensional vector space over a field with 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer?.
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