Mathematics Exam > Mathematics Questions > Which of the following statement is true?a)Th...
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Which of the following statement is true?
- a)There are infinitely many one-one linear transformations from R4 to R3.
- b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.
- c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a linear transformation such that T(B) = A B for every B ∈ Mn( F), then the characteristic polynomial for A is the same as the characteristic polynomial for T.
- d)A two dimensional vector space over a field of 2 elements has exactly 3 different basis.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Which of the following statement is true?a)There are infinitely many o...
(A) We know if T: U → V be a L.T and dim U =m,dim V=n .Then if m>n then then T can not be one-one.
here U = R4 so its dim is 4
and V = R3 so its dim is 3
Thus T can not be one-one
(B) We know if V be a V .S of all n x n, skew symmetric matrices, then
So here n = 4, so dim V = 4.3/2 = 6
(C) Clearly characteristic polynomial of A will be of degree n. while characteristic polynomial of T will be of degree n2.
So they can not be equal.
Thus option A.B,C can not be true,
hence option (D) is correct.
That vector space can have basis as {(1,0),(0,1)} or {(1,1),(0,1)} or {(1,1),(1,0)}
here U = R4 so its dim is 4
and V = R3 so its dim is 3
Thus T can not be one-one
(B) We know if V be a V .S of all n x n, skew symmetric matrices, then
So here n = 4, so dim V = 4.3/2 = 6
(C) Clearly characteristic polynomial of A will be of degree n. while characteristic polynomial of T will be of degree n2.
So they can not be equal.
Thus option A.B,C can not be true,
hence option (D) is correct.
That vector space can have basis as {(1,0),(0,1)} or {(1,1),(0,1)} or {(1,1),(1,0)}
Most Upvoted Answer
Which of the following statement is true?a)There are infinitely many o...
C) let F be a field and A a fixed n x n matrix over F . If T: Mn(F) -> Mn(F) is defined by T(X) = AX, then T is a linear transformation.
This statement is true. The function T is a linear transformation because it satisfies the two properties of linearity: T(cX) = cT(X) for any scalar c and T(X+Y) = T(X) + T(Y) for any matrices X and Y.
This statement is true. The function T is a linear transformation because it satisfies the two properties of linearity: T(cX) = cT(X) for any scalar c and T(X+Y) = T(X) + T(Y) for any matrices X and Y.
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Community Answer
Which of the following statement is true?a)There are infinitely many o...
(A) We know if T: U → V be a L.T and dim U =m,dim V=n .Then if m>n then then T can not be one-one.
here U = R4 so its dim is 4
and V = R3 so its dim is 3
Thus T can not be one-one
(B) We know if V be a V .S of all n x n, skew symmetric matrices, then
So here n = 4, so dim V = 4.3/2 = 6
(C) Clearly characteristic polynomial of A will be of degree n. while characteristic polynomial of T will be of degree n2.
So they can not be equal.
Thus option A.B,C can not be true,
hence option (D) is correct.
That vector space can have basis as {(1,0),(0,1)} or {(1,1),(0,1)} or {(1,1),(1,0)}
here U = R4 so its dim is 4
and V = R3 so its dim is 3
Thus T can not be one-one
(B) We know if V be a V .S of all n x n, skew symmetric matrices, then
So here n = 4, so dim V = 4.3/2 = 6
(C) Clearly characteristic polynomial of A will be of degree n. while characteristic polynomial of T will be of degree n2.
So they can not be equal.
Thus option A.B,C can not be true,
hence option (D) is correct.
That vector space can have basis as {(1,0),(0,1)} or {(1,1),(0,1)} or {(1,1),(1,0)}
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Which of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer?
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Which of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 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 of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 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 of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer?.
Which of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 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 of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 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 of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Which of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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Which of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Which of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Which of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which of the following statement is true?a)There are infinitely many one-one linear transformations from R4 to R3.b)The dimension of the vector space of all 4 x 4 skew symmetric matrices over the field of real no is 10.c)let F be a field and A a fixed n x n matrix over F .lf T: M n( F ) → M n( F ) is a lineartransformation such that T(B) = A B for every B ∈ Mn( F), then the characteristicpolynomial for A is the same as the characteristic polynomial for T.d)A two dimensional vector space over a field of 2 elements has exactly 3 different basis.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Mathematics tests.
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