Engineering Mat...

​The determinant of a 2 × 2 matrix is 100. If one Eigen value of the matrix is 10, the other Eigen value is ________.

Find the value of λ for which the vectors given are linearly dependent:

\(\begin{array}{l} \vec a = i + 2\hat j + 3\hat k\\ \vec b = 4i + \lambda \hat j + 6\hat k\\ \vec c = 3i + 4\hat j + 5\hat k \end{array}\)

Matrix \(A = \left[ {\begin{array}{*{20}{c}} 1&4\\ { - 1}&{ - 2} \end{array}} \right]\) is -Nilpotent matrix of Index -

Let A_{3 × 3} is a real symmetric matrix and λ₁ and λ₂ are the eigen values of the matrix. The corresponding eigen vector is \(\left[ {\begin{array}{*{20}{c}} 2\\ 2\\ \lambda \end{array}} \right]\) and \(\left[ {\begin{array}{*{20}{c}} 1\\ 0\\ 1 \end{array}} \right]\) respectively.

Thus for both λ₁ and λ₂ ≠ 0, the correct value of λ is _____.

If a square matrix \(A = \left[ {\begin{array}{*{20}{c}} 1&2&2\\ 0&2&1\\ { - 1}&2&2 \end{array}} \right]\) then which of the following will be eigenvalue of adj (A)?

Let \(P = \left[ {\begin{array}{*{20}{c}} 1&3\\ 0&1 \end{array}} \right]\) and \(D = \left[ {\begin{array}{*{20}{c}} 2&0\\ 0&{ - 2} \end{array}} \right]\). If A = PDP^-1 then A⁵ is

Find the values of a and b if the equations have a unique solution.

2x + 4y + 5z = 6

2x + 5y + 6z = 7   

2x + 5y + (a+2) z = (b + 2)

If  \(A = \left[ {\begin{array}{*{20}{c}} 1&2&3&4\\ 0&5&6&7\\ 0&0&8&9\\ 0&0&0&{10} \end{array}} \right]\) then the value of \(adj\left( {adj\left( A \right)} \right)\;?\)

Which is not the eigenvector for the given matrix

\(\left[ {\begin{array}{*{20}{c}} 3&1&4\\ 0&2&6\\ 0&0&5 \end{array}} \right]\) ?

Gauss-Seidel method is used to solve the following equations (as per the given order):

x₁ + 2x₂ + 3x₃ = 5

2x₁ + 3x₂ + x₃ = 1

3x₁ + 2x₂ + x₃ = 3