1
GATE CSE 1996
+1
-0.3
Let AX = B be a system of linear equations where A is an m x n matrix and B is a $$m\,\, \times \,\,1$$ column vector and X is a n x 1 column vector of unknowns. Which of the following is false?
A
The system has a solution if and only if, both A and the augmented matrix [A B] have the same rank.
B
If m < n and B is the zero vector, then the system has infinitely many solutions.
C
If m = n and B is a non zero vector, then the system has a unique solution.
D
The system will have only a trivial solution when m = n, B is the zero vector and rank (A) = n
2
GATE CSE 1996
Subjective
+1
-0
Let $$A = \left[ {\matrix{ {{a_{11}}} & {{a_{12}}} \cr {{a_{21}}} & {{a_{22}}} \cr } } \right]\,\,$$ and $$B = \left[ {\matrix{ {{b_{11}}} & {{b_{12}}} \cr {{b_{21}}} & {{b_{22}}} \cr } } \right]\,\,$$ be
two matrices such that $$AB=1.$$
Let $$C = A\left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]$$ and $$CD=1.$$
Express the elements of $$D$$ in terms of the elements of $$B.$$
3
GATE CSE 1995
+1
-0.3
The rank of the following (n + 1) x (n + 1) matrix, where a is a real number is $$\left[ {\matrix{ 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr . & . & . & . & . & . & . \cr . & . & . & . & . & . & . \cr . & . & . & . & . & . & . \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr } } \right]$$$A 1 B 2 C n D Depends on the value of a 4 GATE CSE 1995 MCQ (Single Correct Answer) +1 -0.3 The rank of the following (n + 1) x (n + 1) matrix, where a is a real number is $$\left[ {\matrix{ 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr . & . & . & . & . & . & . \cr . & . & . & . & . & . & . \cr . & . & . & . & . & . & . \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr } } \right]$$$
A
1
B
2
C
n
D
Depends on the value of a
GATE CSE Subjects
EXAM MAP
Medical
NEET