Engineering Mat...

Consider the matrix A_{7 × 5}, B_{7 × 5} and C_{4 × 5}. The order of [C(A^TB)^-1C^T]^T

Consider a 7 × 4 matrix  in which all the matrix element is equal to \(x\) where \(x\)is an integer?

What is the rank of 7 × 4 matrix?

For a matrix [M] \(= \left[ {\begin{array}{*{20}{c}} {\frac{3}{5}}&{\frac{4}{5}}\\ x&{\frac{3}{5}} \end{array}} \right]\), the transpose of the matrix is equal to the inverse of the matrix [M]^T = [M]^-1. The value of x is given by

Consider a matrix A which is singular

\(A =\left[ {\begin{array}{*{20}{c}} 8&0&0&0\\ 9&{11}&13&{15}\\ 19&0&15&5\\ {11}&0&a&18 \end{array}} \right]\)

What is the value of a?

What is the rank of the below given matrix?

\(X = \;\left[ {\begin{array}{*{20}{c}}5&7&2&1\\1&1&{ - 8}&1\\2&3&5&0\\3&4&{ - 3}&1\end{array}} \right]\)

Consider a 4 × 4 Matrix given below

\(\left[ {\begin{array}{*{20}{c}} 4&16&1&{64}\\ 5&25&{1}&{125}\\ 8&64&{1}&{512}\\ 10&100&{1}&{1000} \end{array}} \right]\) 

What is the determinant of the above matrix?

The maximum value of the determinant among all 2 × 2 real symmetric matrices with trace 24 is _______.

If \(A = \left[ {\begin{array}{*{20}{c}} 2&5&7\\ \lambda &{10}&{4\lambda - 2}\\ {\lambda + 4}&{4 + {\lambda ^2}}&{2{\lambda ^2} - 4} \end{array}} \right]\) then for what value of λ, rank of A is 1.

Given that

\(M = \;\left[ {\begin{array}{*{20}{c}}{ - 3}&4\\{ - 1}&2\end{array}} \right];\;and\;I = \;\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]\)

the value of M³ is

Consider the determinant of the matrix \(A =\left[ {\begin{array}{*{20}{c}} 2&5&3\\ 7&8&{ 1}\\ 0&7&4 \end{array}} \right]\)  be \(x\), and the determinant of the matrix \(B =\left[ {\begin{array}{*{20}{c}} 0&7&4\\ 7&8&{ 1}\\ 2&5&3 \end{array}} \right]\) be \(y\) then the value of \(x\times y~?\)