In the matrix equation Px = q, which of the following is a necessary condition for the existence of at least one solution for the unknown vector x

In the matrix equation Px = q, which of the following is a necessary condition for the existence of at least one solution for the unknown vector x Correct Answer Augmented matrix must have the same rank as matrix P

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Consider a system described by ẋ = Ax + Bu y = Cx + Du The system is completely output controllable if and only if Where: x = State vector (n-vector) u = Control vector (r-vector) y = Output vector (m-vector) A = n × n matrix B = n × r matrix C = m × n matrix D = m × r matrix
In the matrix equation Px = q, which of the following is a necessary condition for existence of at least one solution for unknown vector x?