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GATE 2020 : Engg. Mathematics Quiz 4
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Question 1
The larger of the two Eigen values of the matrix
Question 2
Let where and w are unknown. Suppose is an eigen vector of A, then find the corresponding Eigen value.
Question 3
A non-zero polynomial f(x) of degree 3 has roots at x = 1, x = 2 and x = 3. Which one of the following must be TRUE?
Question 4
Consider the following system of equations in three real variables xl, x2 and x3
2x1 – x2 + 3x3 = 1
3x1– 2x2 + 5x3 = 2
–x1 + 4x2 + x3 = 3
This system of equations has
2x1 – x2 + 3x3 = 1
3x1– 2x2 + 5x3 = 2
–x1 + 4x2 + x3 = 3
This system of equations has
Question 5
If the following system has non-trivial solution,
px+ qy+ rz= 0
qx+ ry+ pz= 0
rx+ py+ qz= 0,
then which one of the following options is TRUE?
px+ qy+ rz= 0
qx+ ry+ pz= 0
rx+ py+ qz= 0,
then which one of the following options is TRUE?
Question 6
Let A be a 4 × 4 matrix with eigenvalues -5, -2, 1, 4. Which of the following is an eigen value of where I is the 4 × 4 identity matrix?
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