5) the equation ax = 5 is consistent, if and only if ū is in the span of columns of matrix a. 6) a linear transformation x + ax is one-to-one if the equation ax = 5 is always consis- tent. 7) a linear transformation x + ax is onto, if columns of matrix a span codomain of the transformation. 8) if the columns of matrix a is linearly independent, then the linear transformation x ax is one-to-one. every non-zero n x n matrix a is invertible. ) if a linear transformation x ax is one-to-one and onto, then the matrix a is invert-

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

step-by-step explanation:   divide the numerator by the denominator to get the decimal

it would still be 193

if divide by 100 then 1.93

i am not sure