Engineering Mat...

The number of distinct real values of x for which the matrix \(\left( {\begin{array}{*{20}{c}} x&1&1\\ 1&x&1\\ 1&1&x \end{array}} \right)\) is singular is

2x + 3y + 5z = 9

7x + 3y – 2z = 8

2x + 3y + λz = 7

If \(A\left[ {\begin{array}{*{20}{c}}1&1\\{ - 1}&1\end{array}} \right]\) and A⁴ = kI, where I is identity matrix

The Eigen values of the matrix \(\left[ {\begin{array}{*{20}{c}}3&0&0\\0&2&{ - 3}\\0&1&{ - 2}\end{array}} \right]\) are

The matrix \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} {\rm{a}}&0&3&7\\ 2&5&1&3\\ 0&0&2&4\\ 0&0&0&{\rm{b}} \end{array}} \right]\) has \(\rm det(A) = 100\) and \(\rm trace(A) = 14\).

Find the Eigen vector of matrix A corresponding to highest Eigen value.

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

Find the value of x and y for the below given simultaneous equations if it has no solutions?

a + b + c = 18

2a + 4b + 6c = 12

Find the matrix A if

\(\left[ {\begin{array}{*{20}{c}}2&1\\3&2\end{array}} \right]A\left[ {\begin{array}{*{20}{c}}{ - 3}&2\\5&{ - 3}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{ - 2}&4\\3&{ - 1}\end{array}} \right]\)

If \(A = \left[ {\begin{array}{*{20}{c}}2&{ - 3}\\1&{ - 1}\end{array}} \right]\) then what is |A¹⁰⁰⁹ – 5 A¹⁰⁰⁸| = ?

Let \(P = \left[ {\begin{array}{*{20}{c}}1&1&{ - 1}\\2&{ - 3}&4\\3&{ - 2}&3\end{array}} \right]\;and\;Q = \left[ {\begin{array}{*{20}{c}}{ - 1}&{ - 2}&{ - 1}\\6&{12}&6\\5&{10}&5\end{array}} \right]\) be two matrices.

Then the rank of P + Q is ______.