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

question 45

Multiple Choice

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) \(2 \mathrm { k } , ( - 2 ) ^ { \mathrm { k } } , ( - 4 ) ^ { \mathrm { k } }\)

---

Definitions:

Worries

Thoughts or concerns about potential problems or dangers, which can affect individuals' mental and emotional well-being.

Adjusting

The process of modifying or altering behavior, practices, or attitudes to better suit new conditions or environments.

Remarriage

The act of marrying again after a divorce or the death of a spouse.

Adolescents

Individuals in the transitional stage of physical and psychological development that typically occurs during the period from puberty to legal adulthood.