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Q#1
Linear Algebra
GATE EC 2025
MCQ
+1 mark
-0.33 marks
Consider the matrix 
below:
For which of the following combinations of 
, and 
, is the rank of at least three?
(i) 
and 
.
(ii) 
.
(iii) 
and 
.
(iv) 
.
Only (i), (iii), and (iv)
Only (iv)
Only (ii)
Only (i) and (iii)
Explanation:
The given matrix is in standard Echelon form,
rank of matrix 
if or 
rank of matrix = 4 if or and 
Thus, (i), (iii), (iv) satisfy the echelon form requirement
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