If a is a diagonalizable matrix, a) prove that a^t is diagonalizable. b) prove that a^-1 is diagonalizable. c) prove that a^2 is diagonalizable. d) prove that a^k is diagonalizable for any positive integer k.

so, converting firstly the mixed fractions to improper fractions and then "adding".

what statement? is there an image?

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4