Mathematics Exam > Mathematics Questions > Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D...
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Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.
Following statements are made with respect to these matrices.
1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.
2. Matrix product [D]T [F] [D] is always symmetric.
With reference to above statements, which of the following applies?
Following statements are made with respect to these matrices.
1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.
2. Matrix product [D]T [F] [D] is always symmetric.
With reference to above statements, which of the following applies?
- a)Statement 1 is true but 2 is false
- b)Statement 1 is false but 2 is true
- c)Both the statements are true
- d)Both the statements are false
Correct answer is option 'A'. Can you explain this answer?
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Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5...
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Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5...
Statement 1: Matrix product [F]T [C]T [B] [C] [F] is a scalar.
To determine whether the given matrix product is a scalar, we need to analyze the dimensions of the matrices involved and check if they align properly for multiplication.
Let's break down the matrix product step by step:
1. [F]T [C]T: The transpose of [F] is a 1 x 5 matrix, and the transpose of [C] is a 5 x 3 matrix. So, the product [F]T [C]T will be a 1 x 3 matrix.
2. [F]T [C]T [B]: The dimensions of the result from step 1 are 1 x 3, and [B] is a 3 x 3 matrix. So, the product [F]T [C]T [B] will be a 1 x 3 matrix.
3. [F]T [C]T [B] [C]: The dimensions of the result from step 2 are 1 x 3, and [C] is a 3 x 5 matrix. So, the product [F]T [C]T [B] [C] will be a 1 x 5 matrix.
4. [F]T [C]T [B] [C] [F]: The dimensions of the result from step 3 are 1 x 5, and [F] is a 5 x 1 matrix. So, the product [F]T [C]T [B] [C] [F] will be a scalar.
Hence, statement 1 is true.
Statement 2: Matrix product [D]T [F] [D] is always symmetric.
To determine the symmetry of the matrix product [D]T [F] [D], we need to analyze the dimensions of the matrices involved and check if they align properly for multiplication.
Let's break down the matrix product step by step:
1. [D]T [F]: The transpose of [D] is a 3 x 5 matrix, and [F] is a 5 x 1 matrix. So, the product [D]T [F] will be a 3 x 1 matrix.
2. [D]T [F] [D]: The dimensions of the result from step 1 are 3 x 1, and [D] is a 5 x 3 matrix. So, the product [D]T [F] [D] will be a 3 x 3 matrix.
To determine whether the matrix product [D]T [F] [D] is symmetric, we need to check if it is equal to its transpose.
If [D]T [F] [D] is symmetric, then ([D]T [F] [D])T = [D]T [F] [D].
Taking the transpose of [D]T [F] [D], we get ( [D]T [F] [D] )T = [D]T [F]T [D]T.
Since [F]T is a 1 x 5 matrix and [D]T is a 3 x 5 matrix, their product [F]T [D
To determine whether the given matrix product is a scalar, we need to analyze the dimensions of the matrices involved and check if they align properly for multiplication.
Let's break down the matrix product step by step:
1. [F]T [C]T: The transpose of [F] is a 1 x 5 matrix, and the transpose of [C] is a 5 x 3 matrix. So, the product [F]T [C]T will be a 1 x 3 matrix.
2. [F]T [C]T [B]: The dimensions of the result from step 1 are 1 x 3, and [B] is a 3 x 3 matrix. So, the product [F]T [C]T [B] will be a 1 x 3 matrix.
3. [F]T [C]T [B] [C]: The dimensions of the result from step 2 are 1 x 3, and [C] is a 3 x 5 matrix. So, the product [F]T [C]T [B] [C] will be a 1 x 5 matrix.
4. [F]T [C]T [B] [C] [F]: The dimensions of the result from step 3 are 1 x 5, and [F] is a 5 x 1 matrix. So, the product [F]T [C]T [B] [C] [F] will be a scalar.
Hence, statement 1 is true.
Statement 2: Matrix product [D]T [F] [D] is always symmetric.
To determine the symmetry of the matrix product [D]T [F] [D], we need to analyze the dimensions of the matrices involved and check if they align properly for multiplication.
Let's break down the matrix product step by step:
1. [D]T [F]: The transpose of [D] is a 3 x 5 matrix, and [F] is a 5 x 1 matrix. So, the product [D]T [F] will be a 3 x 1 matrix.
2. [D]T [F] [D]: The dimensions of the result from step 1 are 3 x 1, and [D] is a 5 x 3 matrix. So, the product [D]T [F] [D] will be a 3 x 3 matrix.
To determine whether the matrix product [D]T [F] [D] is symmetric, we need to check if it is equal to its transpose.
If [D]T [F] [D] is symmetric, then ([D]T [F] [D])T = [D]T [F] [D].
Taking the transpose of [D]T [F] [D], we get ( [D]T [F] [D] )T = [D]T [F]T [D]T.
Since [F]T is a 1 x 5 matrix and [D]T is a 3 x 5 matrix, their product [F]T [D
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Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. Can you explain this answer?
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Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. 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 Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. Can you explain this answer?.
Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. 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 Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Real matrices [A]3 x 1, [B]3 x 3, [C]3 x 5,[D]5 x 3, [E]5 x 5 and [F]5 x 1 are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.1. Matrix product [F]T [C]T [B] [C] [F] is a scalar.2. Matrix product [D]T [F] [D] is always symmetric.With reference to above statements, which of the following applies?a)Statement 1 is true but 2 is falseb)Statement 1 is false but 2 is truec)Both the statements are trued)Both the statements are falseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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