Question

Let P and Q be matrices of size 4X6 and 4X1, respectively which of the following is
correct for the system of linear equations Px=Q?
A) If the system is consistent then it has infinitely many solutions.
B) IfQ=0 then the system is inconsistent.
C) If Q+0 and the system is consistent, then the rank of P must be 6.
D) IfQ=0, then the system has a unique solution.​

Answer 1

Answer:

A

Explanation:

as I dont know the answer. please some one tell the right answer

Answer 2

Answer:

The Correct answer is option A

Explanation:

Concept:

• The equation $P x=q$ will have at least one solution only if it is consistent.
• The given system will be consistent only if $Rank [Pq] = Rank [P].$

Note:

So, a necessary condition for the existence of at least one solution for unknown vector $x$ is that the augmented matrix [Pq] must have the same rank as matrix $P$.

Additional Information

A consistent solution means either the system has a unique solution or infinitely many solutions. So,

1. the matrix $P x=q$ will have a unique solution if Rank $[P q]=Rank}[P]=$ $\mathbf{m} , where ' m ' is of order of matrix P , and$

2. the matrix $P x=q$ will have infinitely many solutions if Rank $[P q]= Rank[\mathrm{P}] < \mathrm{m} .$