Determine if the columns of the matrix form a linearly independent set. Justify your answer. [Start 3 By 4 Matrix 1st Row 1st Column 1 2nd Column negative 2 3rd Column 2 4st Column 3 2nd Row 1st Column negative 2 2nd Column 4 3rd Column negative 4 4st Column 3 3rd Row 1st Column 0 2nd Column 1 3rd Column negative 1 4st Column 4 EndMatrix ]1 −2 2 3 −2 4 −4 3 0 1 −1 4 Choose the correct answer below. A. The columns of the matrix do form a linearly independent set because there are more entries in each vector than there are vectors in the set

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

3

step-by-step explanation:

i believe a. 12x≥120 is the answer

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