List of top Mathematics for Economy Questions on Linear Algebra asked in IIT JAM EN

For 𝛼 , 𝛽 ∈ R, consider the system of linear equations
𝑥 + 𝑦 + 𝑧 = 1 
3𝑥 + 𝑦 + 2𝑧 = 2 
5x + 𝛼𝑦 + 𝛽𝑧 = 3 
Then

For α, β ∈ R , α ≠ β, if −2 and 5 are the eigenvalues of the matrix 𝑀=[1−𝛼1+𝛽𝛽 𝛼+𝛽] and 𝑋 = [𝑥1 𝑥2 ] is an eigenvector of 𝑀 associated to −2, then\(M=\begin{bmatrix} 1-α& 1+β\\ β & a+B& \end{bmatrix}\)
and 𝑋 = \(\begin{bmatrix}  X_1\\ X_2 \end{bmatrix}\) is an eigenvector of 𝑀 associated to −2, then

Let 𝑀 = \(\begin{bmatrix} K & 1 & 1 \\ 1 & K & 1 \\ 1 & 1 & K \end{bmatrix}\)and I₃ be the identity matrix of order 3. If the rank of the matrix 10 𝐼₃ − 𝑀 is 2 then 𝑘 is equal to _____ (in integer).

Choose the option that represents the original linear programming problem based on the initial simplex tableau given below, where \(S_i\) represents slack/surplus variables and \(A_i\) represents the artificial variables corresponding to the \(i^{th}\)constraint: 

Which of the following statements is CORRECT for Game A and Game B?

Game A: Mary wants to watch a movie and John is interested in watching a football match. Both wish to be together. The payoff matrix is:

Game B: The Prisoner's dilemma problem is shown below:

The sum of the eigen values of the square matrix $ \begin{pmatrix} {1} & {1} & {3}\\ {1} & {5} & {1}\\ {3} & {1} & {1} \end{pmatrix}$ (in integer).

Let the linear programming problem be
Maximize Z = - 0.2x₁ + x₂
subject to 2x₁ + 5x₂ ≤ 70,
x₁ + x₂ ≤ 20,
x₁, x₂ ≥ 0.
If x₁ = a and x₂ = b is the optimal solution, then a+b=______ (in integer).