Engineering Mat...

In the equation \(AX = B,\;A = \left[ {\begin{array}{*{20}{c}}{\frac{1}{{\sqrt 2 }}}&0&{\frac{1}{{\sqrt 2 }}}\\0&1&0\\{\frac{1}{{\sqrt 2 }}}&0&{\frac{{ - 1}}{{\sqrt 2 }}}\end{array}} \right],\;X = \left[ {\begin{array}{*{20}{c}}x\\y\\z\end{array}} \right],B = \left[ {\begin{array}{*{20}{c}}0\\1\\{ - \sqrt 2 }\end{array}} \right]\), where A is an orthogonal matrix, the sum of the unknowns, x + y + z = _______

Let \(A = \left( {\begin{array}{*{20}{c}} 1&1&1&1\\ 1&2&{ - 1}&\lambda \\ 5&{ 7}&1&{{\lambda ^2}} \end{array}} \right),\;\lambda \in R\). The rank of A is 2 if λ = _____

The value of t so that \(\left[ {\begin{array}{*{20}{c}} 4\\ { - 1} \end{array}} \right]\) is an eigen vector of \(\left[ {\begin{array}{*{20}{c}} 3&4\\ 2&t \end{array}} \right]\) is ______

For the system of linear equations

x + 3y – 2z = -1

5y + 3z = -8

x – 2y – 5z = 7

The determinant value of \(A = \left[ {\begin{array}{*{20}{c}} {\cos x}&{ - \sin x}&1\\ {\sin x}&{\cos x}&1\\ {\cos \left( {x + y} \right)}&{ - \sin \left( {x + y} \right)}&0 \end{array}} \right]\) lies in the interval

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

Consider the following system of equations in x, y, z:

x + 2y + 2z = 1

x + ay + 3z = 3

x + 11y + az = b

Consider the 2 × 2 matrix \(A = \left[ {\begin{array}{*{20}{c}}2&3\\x&4\end{array}} \right]\). What is the maximum value of x, for which both the Eigen values of matrix are real and positive?

If \(A = \left[ {\begin{array}{*{20}{c}} 1&0&0\\ i&{\frac{{ - 1 + i\sqrt 3 }}{2}}&0\\ 0&{1 + 2i}&{\frac{{ - 1 - i\sqrt 3 }}{2}} \end{array}} \right]\) then the trace of A¹⁰² is

If \(A = \left[ {\begin{array}{*{20}{c}}1&1&3\\5&2&6\\{ - 2}&{ - 1}&{ - 3}\end{array}} \right]\), then the value of A¹⁴ + 3A – 2I is