Electrical Engineering > GATE 2026 > Linear Equations
Consider the system of linear equations: Ax = b, where A is an n × n matrix, and x and b are n-dimensional column vectors.
Suppose this system of equations has a unique solution. Which of the following statements is/are correct?
A
A−1 exists
B
The system of equations Amx = b also has a unique solution for m = 1, 2, 3,...
C
rank(A) = rank(Am), for m = 1, 2, 3,...
D
rank(A) < rank([A|b]), where [A|b] denotes the augmented matrix.

Correct : a,c

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linear algebra GATE 2026 matrix inverse unique solution system rank matrix augmented matrix GATE electrical engineering gate linear equations unique solution GATE 2026 electrical matrix rank equations

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