\( X=\left[\begin{array}{rr}x+y-1 & 0 \\ 0 & 3\end{array}\right] \) and \( Y=\left[\begin{array}{rr}5 & 0 \\ 0 & 2 x-3 y-7\end{array}\right] \) The value(s) of \( y \) for which the matrices \( X^{T} \) and \( Y \) have no inverses is/are given by: \( \begin{array}{l}k=\frac{2}{5} \\ \\ y=-2\end{array} \) and \( y=k \) \( y=1 \)

حل معادله نمایی \( 2^{x} = 16 \) را با استفاده از لگاریتم‌ها به دست آورید.

(b) (i) If the polynomial \( f(x)=2 x^{3}+p x^{2}+q x+1 \) has a factors \( 2 x-1 \) and \( x \mp 1 \). Find the values of \( p \) and \( q \). (ii) In the expansion of \( (1+p x)^{n} \) in the ascending power of \( x \), the second term is \( 18 x \) and the thited term is \( 135 x^{2} \). Find the values of \( n \) and \( p \)

(b) Solve the following equation by factorizat \[ 2 x^{2}-9 x=0 \]

If a line goes up from left to right, what can you say about its slope? Give an example.

\( y-4)^{2}+y^{2}-4 y+4 \) при \( y=\frac{9}{4} \)