Studdy AI Logo
Math  /  Algebra

Question23. Let A=[−612−36]A=\left[\begin{array}{rr}-6 & 12 \\ -3 & 6\end{array}\right] and w=[21]w=\left[\begin{array}{l}2 \\ 1\end{array}\right]. Determine if ww is in Col Al Is in in Nol A?
24. Let A=[−8−2−9648404]A=\left[\begin{array}{rrr}-8 & -2 & -9 \\ 6 & 4 & 8 \\ 4 & 0 & 4\end{array}\right] and w=[21−2]w=\left[\begin{array}{r}2 \\ 1 \\ -2\end{array}\right]. Determine if w is in ColA\mathrm{Col} A. Is w in Nul A?
In Exercises 15 and 16 , find AA ouch that the given set is Col⁡A\operatorname{Col} A
15. {[2s+3tr+s−2t4r+s3r−s−t]:r,s,t\left\{\left[\begin{array}{c}2 s+3 t \\ r+s-2 t \\ 4 r+s \\ 3 r-s-t\end{array}\right]: r, s, t\right. real }\}
16. {[b−c2b+c+d5c−4dd]:b,c,d\left\{\left[\begin{array}{c}b-c \\ 2 b+c+d \\ 5 c-4 d \\ d\end{array}\right]: b, c, d\right. real }\}

Studdy Solution
The columns of A A are the coefficients of b,c,d b, c, d :
A=[1−1021105−4001]A = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 1 & 1 \\ 0 & 5 & -4 \\ 0 & 0 & 1 \end{bmatrix}
The solutions to the problems are as follows: - Problem 23: w w is in both Col⁡A\operatorname{Col} A and Nul⁡A\operatorname{Nul} A. - Problem 24: Check row reduction for Col⁡A\operatorname{Col} A and compute Aw Aw for Nul⁡A\operatorname{Nul} A. - Problem 15: A=[02311−24103−1−1] A = \begin{bmatrix} 0 & 2 & 3 \\ 1 & 1 & -2 \\ 4 & 1 & 0 \\ 3 & -1 & -1 \end{bmatrix} . - Problem 16: A=[1−1021105−4001] A = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 1 & 1 \\ 0 & 5 & -4 \\ 0 & 0 & 1 \end{bmatrix} .

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord