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A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain a unique solution by multiplying both left and right sides of the equation by AT (the super script T denotes the transpose) and inverting the matrix AT A? Answer is
- a)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.
- b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.
- c)Yes, can obtain a unique solution provided the matrix AT A is well conditioned
- d)Yes, can obtain a unique solution provided the matrix A is well conditioned.
Correct answer is option 'B'. Can you explain this answer?
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A set of linear equations is given in the form Ax = b, where A is a 2 ...
From the properties of a matrix,
The rank of m × n matrix is always ≤ min {m, n}
If the rank of matrix A is ρ(A) and rank of matrix B is ρ(B), then the rank of matrix AB is given by
ρ(AB) ≤ min {ρ(A), ρ(B)}
If n × n matrix is singular, the rank will be less than ≤ n
Given:
AX = B
Where A is 2 × 4 matrices and b ≠ 0
The order of AT is 4 × 2
The order of ATA is 4 × 4
Rank of (A) ≤ min (2, 4) = 2
Rank of (AT) ≤ min (2, 4) = 2
Rank (ATA) ≤ min (2, 2) = 2
As the matrix ATA is of order 4 × 4, to have a unique solution the rank of ATA should be 4.
Therefore, the unique solution of this equation is not possible.
The rank of m × n matrix is always ≤ min {m, n}
If the rank of matrix A is ρ(A) and rank of matrix B is ρ(B), then the rank of matrix AB is given by
ρ(AB) ≤ min {ρ(A), ρ(B)}
If n × n matrix is singular, the rank will be less than ≤ n
Given:
AX = B
Where A is 2 × 4 matrices and b ≠ 0
The order of AT is 4 × 2
The order of ATA is 4 × 4
Rank of (A) ≤ min (2, 4) = 2
Rank of (AT) ≤ min (2, 4) = 2
Rank (ATA) ≤ min (2, 2) = 2
As the matrix ATA is of order 4 × 4, to have a unique solution the rank of ATA should be 4.
Therefore, the unique solution of this equation is not possible.
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A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer?
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A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer?.
A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer?.
Solutions for A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain aunique solutionby multiplying both left and right sides of the equation by AT(the super script T denotes the transpose) and inverting the matrix ATA? Answer isa)Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.b)No, it is not possible to get a unique solution for any 2 × 4 matrix A.c)Yes, can obtain a unique solution provided the matrix ATA is well conditionedd)Yes, can obtain a unique solution provided the matrix A is well conditioned.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
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