Find the new coordinate vector for the vector x after performing the specified change of basis.
-$y \mathrm { k } + 3 - 4 \mathrm { y } _ { \mathrm { k } } + 2 - 4 \mathrm { y } \mathrm { k } + 1 + 16 \mathrm { y } _ { \mathrm { k } } = 0$ for all $\mathrm { k }$
A) $2 \mathrm { k } , 4 \mathrm { k } , ( - 2 ) ^ { \mathrm { k } } , ( - 3 ) ^ { \mathrm { k } }$
B) $2 \mathrm { k } , 4 \mathrm { k } , ( - 2 ) ^ { \mathrm { k } }$
C) $2 \mathrm { k } , 4 \mathrm { k }$
D) $2 \mathrm { k } , ( - 2 ) ^ { \mathrm { k } } , ( - 4 ) ^ { \mathrm { k } }$

Question

Quizplus · Accepted Answer

The correct answer is A because the given equation is a linear combination of the basis vectors $2 \mathrm { k } , 4 \mathrm { k } , ( - 2 ) ^ { \mathrm { k } } , ( - 3 ) ^ { \mathrm { k } }$.

Find the New Coordinate Vector for the Vector X After yk+3−4yk+2−4yk+1+16yk=0y \mathrm { k } + 3 - 4 \mathrm { y } _ { \mathrm { k } } + 2 - 4 \mathrm { y } \mathrm { k } + 1 + 16 \mathrm { y } _ { \mathrm { k } } = 0yk+3−4yk​+2−4yk+1+16yk​=0

Find the New Coordinate Vector for the Vector X After $y \mathrm { k } + 3 - 4 \mathrm { y } _ { \mathrm { k } } + 2 - 4 \mathrm { y } \mathrm { k } + 1 + 16 \mathrm { y } _ { \mathrm { k } } = 0$