Consider the matrices $$\,{X_{4x3,}}\,\,{Y_{4x3}}$$ $$\,\,{P_{2x3}}.$$ The order of $$\,{\left[ {P{{\left( {{X^T}Y} \right)}^{ - 1}}{P^T}} \right]^T}$$ will be

Consider the system of equations, $${A_{nxn}}\,\,{X_{nx1}}\,\, = \lambda \,{X_{nx1}}$$ where $$\lambda $$ is a scalar. Let $$\left( {{\lambda _i},\,\,{X_i}} \right)$$ be an eigen value and its corresponding eigen vector for real matrix $$A$$. Let $${{\rm I}_{nxn}}$$ be unit matrix. Which one of the following statement is not correct?

Value of the integral $$\,\,\oint {xydy - {y^2}dx,\,\,} $$ where, $$c$$ is the square cut from the first quadrant by the line $$x=1$$ and $$y=1$$ will be (Use Green's theorem to change the line integral into double integral)

Transformation to linear form by substituting $$v = {y^{1 - n}}$$ of the equation $${{dy} \over {dt}} + p\left( t \right)y = q\left( t \right){y^n},\,\,n > 0$$ will be