1
GATE CSE 1998
MCQ (Single Correct Answer)
+1
-0.3
Consider the following set a equations
x + 2y = 5
4x + 8y = 12
3x + 6y + 3z = 15 This set
A
has a unique solution
B
has no solutions
C
has finite number of solutions
D
has infinite number of solutions
2
GATE CSE 1997
MCQ (Single Correct Answer)
+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
3
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
4
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 $$B.$$
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