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A is a 3 x 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
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A is a 3 x 4 real matrix and A x = b is an inconsistent system of equa...
The highest possible rank of matrix A in an inconsistent system of equations can be determined by performing row reduction or using the concept of linear independence.
In an inconsistent system of equations, there are no solutions that satisfy all the equations simultaneously. This implies that at least one row of the coefficient matrix A must be a linear combination of the other rows.
Since A is a 3 x 4 real matrix, the highest possible rank of A cannot exceed the number of rows, which is 3. However, if the system is inconsistent, one row must be a linear combination of the others, resulting in linear dependence.
If one row can be expressed as a linear combination of the other rows, the rank of A will be less than 3. The highest possible rank of A in this case is 2.
Therefore, the correct answer is B: 2.
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A is a 3 x 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?
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