1
GATE CSE 1997
+1
-0.3
The determination of the matrix $$\left[ {\matrix{ 6 & { - 8} & 1 & 1 \cr 0 & 2 & 4 & 6 \cr 0 & 0 & 4 & 8 \cr 0 & 0 & 0 & { - 1} \cr } } \right]\,\,is$$$A 11 B - 48 C 0 D - 24 2 GATE CSE 1996 MCQ (Single Correct Answer) +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 3 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 $$B.$$ 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