Answer to Question #107563 in Algebra for George Mwila Chola

Question

Question One

Matrix P = ( 3 -1 ) and Q = ( 3 4 ) If P and Q have equal determinants find the value of x.
(-2 0 ) (-4 x )

Question Two

Factorise Completely 5X^2 - X - 4

Answer 1

Solution (1)

Determinant of matrix P

$det \space \begin{pmatrix}3&-1\\ -2&0\end{pmatrix}=0-(-1)(-2)=-2$

Determinant of matrix Q

$det \:\begin{pmatrix}3&4\\ \:\:-4&x\end{pmatrix}=3(x)-4(-4)=3x+16$

From question |P| = |Q|

$\Rightarrow -2=3x+16$

$\Rightarrow 3x=-18$

$\Rightarrow x=-18/3 = -6$

Solution (2)

$5x^2-x-4$

$=5x^2-5x+4x-4$

$=5x(x-1)+4(x-1)$

$=(5x+4)(x-1)$