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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?
  • 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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Most Upvoted Answer
A set of linear equations is given in the form Ax = b, where A is a 2 ...
Concept:
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
Calculation:
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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Community Answer
A set of linear equations is given in the form Ax = b, where A is a 2 ...
X2 matrix, x is a column vector of variables, and b is a column vector of constants. The linear equations can be written as:

a11x1 + a12x2 = b1
a21x1 + a22x2 = b2

where a11, a12, a21, a22 are the elements of matrix A, and x1, x2 are the variables.

This system of equations can be solved using various methods, such as substitution, elimination, or matrix inversion. The solution, if it exists, will be a unique solution, no solution, or infinitely many solutions depending on the coefficients and constants in the equations.
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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?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 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?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 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 ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT 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?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 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 ACT 2025 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?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 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?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 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 ACT. Download more important topics, notes, lectures and mock test series for ACT Exam by signing up for free.
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