1
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
Let $$A$$ be and n$$ \times $$n matrix of the folowing form. GATE CSE 2004 Discrete Mathematics - Linear Algebra Question 70 English

What is the value of the determinant of $$A$$?

A
GATE CSE 2004 Discrete Mathematics - Linear Algebra Question 70 English Option 1
B
GATE CSE 2004 Discrete Mathematics - Linear Algebra Question 70 English Option 2
C
GATE CSE 2004 Discrete Mathematics - Linear Algebra Question 70 English Option 3
D
GATE CSE 2004 Discrete Mathematics - Linear Algebra Question 70 English Option 4
2
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
How many solutions does the following system of linear equations have?

- x + 5y = - 1
x - y = 2
x + 3y = 3
A
infinitely many
B
two distinct solutions
C
unique
D
None
3
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6
Consider the following system of linear equations $$$\left[ {\matrix{ 2 & 1 & { - 4} \cr 4 & 3 & { - 12} \cr 1 & 2 & { - 8} \cr } } \right]\left[ {\matrix{ x \cr y \cr z \cr } } \right] = \left[ {\matrix{ \alpha \cr 5 \cr 7 \cr } } \right]$$$

Notice that the second and the third columns of the coefficient matrix are linearly dependent. For how many values of $$\alpha $$, does this system of equations have infinitely many solutions?

A
$$0$$
B
$$1$$
C
$$2$$
D
infinitely many
4
GATE CSE 2002
Subjective
+2
-0
Obtain the eigen values of the matrix $$$A = \left[ {\matrix{ 1 & 2 & {34} & {49} \cr 0 & 2 & {43} & {94} \cr 0 & 0 & { - 2} & {104} \cr 0 & 0 & 0 & { - 1} \cr } } \right]$$$
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