Consider the stacked vectors ai ak bi where a... ak are n-vectors and b counter example. bz are m-vectors. For each case, either prove or provide a (a) Suppose ai ak are linearly independent (we make no assumptions about bi bi). Can we conclude that the stacked vectors c . c are linearly indepndent? (b) Suppose a ak are linearly dependent (we make no assumptions about bi bi). Can we conclude that the stacked vectors c..ck are linearly depndent?

(a) Yes,we can conclude that the vectors C₁,...,C₀ are linearly independent.

(b) No,the vectors C₁,...,C₀ can also be linearly independent. For example, take.

Step-by-step explanation:

Note that I'm using "o" instead of "k" for easier computation ∴ C₀ = Ck

Proof by letting ∝₁,...,∝₀ be scalars such that ∝₁c₁+...+∝₀c₀ = 0 are linearly independent.  see equation in picture.

See attached

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

answer: haha (: i’ll go see what it is

step-by-step explanation: