[1 00001 0 1 0 0 0 1, (2 points each item) Let R = 13 0 1 0 0 (a) Let A be any o

Question

[1 00001 0 1 0 0 0 1, (2 points each item) Let R = 13 0 1 0 0 (a) Let A be any other matrix with 5 rows. Explain in words what multiplying A on the left by R does to the rows of A. (b) Explain in words what you would do to undo the effect of multiplying A on the left by R (c) Without doing any computations, write down the inverse of R. (d) Note that (RTA)T = AT((RT)T-ATR. Let C be any matrix with 5 columns. Explain in words what multiplying C on the right by R does to the columns of C. 10 0 0 0 (e) How would your answers to parts (a), (b) and (c) change for R- 3 0 1 0 0

Explanation / Answer

(a) by multiplying on left side the first ,second and 4th row will remain same as A.but 3rd row of multiplication will written by = 3 times of 1st row +third row.

fifth row of multiplication=2 time of 4th row+ fifth row of A

(2) in the multiplication we will apply these operations

.

R3>R3-3R1 and R5-->R5-2R4

using the above transformation

4) In the multiplication RC , the 2nd,3rd and 5th column will be same..as C

first column of RC= C1+3C3

and Fourth column of RC =C4+2C5

and 5) wewe caccacaccaccacacaccacaccaccaccaccacaccaccacacaccacaccacca

3)inverse Matrix of R 1 0 0 0 0 0 1 0 0 0 -3 0 1 0 0 0 0 0 1 0 0 0 0 -2 1

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