Academic Reasoning 1

Question 1

https://gyazo.com/d8b20124750d39de1d271f2afb5a4989

Answer 1

https://gyazo.com/6d32ef7d749707d57ef1950edb489e18

Question 2

https://gyazo.com/088d20de9a35438afd035824c206dd0d

Answer 2

A linear system is consistent if and only if the rightmost column of the augmented matrix is not a pivot column- that is, if and only if an echelon form of the augmented matrix has no row form [0 …. 0 b] with b non zero.
If a linear system is consistent than the only solution set contains either (i) a unique solution, when there are no free variables, or (ii) indefinitely many solutions, when there is at least one free variable. Theorem 2 page 37

Question 3

https://gyazo.com/351282720301d1224477a4cfbc2e2927

Answer 3

https://gyazo.com/aa4699da9703afc09284177c468f751e

Question 4

https://gyazo.com/9e8f998124eed3ab9a7faae0f2cc2bb4

Answer 4

https://gyazo.com/e8080748ea4a2a4623fdf692dab410d1

Question 5

https://gyazo.com/f82578e0e0d25989b336425117236d24

Answer 5

https://gyazo.com/df2bc3f96ae740a652c82f0a2909ebab

Question 6

bhttps://gyazo.com/6ddbf0ca98691cead6ded7f28b0eda60

Answer 6

book 1.5

Question 7

https://gyazo.com/7a16767c488ef9472ce1b2530073338d

Answer 7

https://gyazo.com/861077431763f9bc8e328f1490192c9b

Question 8

https://gyazo.com/0dd865ad22b30d6466185d45bc89f511

Answer 8

https://gyazo.com/cd464619a4ad86c0c27e75bdb4edfcc2

Question 9

https://gyazo.com/8c4c4fe6d7247504e8066e5aa1076e36

Answer 9

https://gyazo.com/ea9121a2d180ae757f8a9001b63ca630

Question 10

https://gyazo.com/8161e7c18071d6586999ac1a930e655e

Answer 10

https://gyazo.com/9bca2bb8fc9636852d1002c581fe38ff

Question 11

https://gyazo.com/bc58d9a49f9c1ba1b31f816a98d627b9

Answer 11

https://gyazo.com/854f5d7d3568a3d0e4302091961a221e

Question 12

https://gyazo.com/24d2f34964ac924e80bb62beb29105b2

Answer 12

https://gyazo.com/53f16bf27fbff93f1a6b5a3c9fcec7ef

Question 13

https://gyazo.com/d860775f169132b4547d9110a3893ba4

Answer 13

qhttps://gyazo.com/d4adb165742067cb0a9610e9f0e115a3

Question 14

https://gyazo.com/e8630a2884d9d4acabaf3860ec8fc122

Answer 14

https://gyazo.com/cd421fe055270a8c7355f4180d3d01a4

Question 15

https://gyazo.com/47fe1dcf1dfe28ec811b69f74a5215ba

Answer 15

https://gyazo.com/1d0ef4c6501dc5be5ac6aa78dd00abd5

Question 16

https://gyazo.com/da768e4c651cc881d266a9736c61192c

Answer 16

https://gyazo.com/acded05ac7ce93aa2c4ce8c90360354c

Question 17

https://gyazo.com/444e8f22163432d173110db522db50b0

Answer 17

https://gyazo.com/c3cff7f1af897a453b84879ff34a4c5e

Question 18

https://gyazo.com/50f1e6caa9b13f4d60dba50a90626f53

Answer 18

https://gyazo.com/78e67a4277fe4d05803497f700ea26c8

Question 19

https://gyazo.com/925e0584262c357dc33ab1f78e46f6f1

Answer 19

https://gyazo.com/f86b6fa3d4637673f37214328336d61b

Question 20

https://gyazo.com/95a8f3f5fcf0b7ece300aa552d20c01b

Answer 20

https://gyazo.com/75695e238d084576cad2ec5584ecfc74

Question 21

https://gyazo.com/460b47d1e5e7551377f809fa7d1a8974

Answer 21

https://gyazo.com/4293502456596aa65524b7d8f289e46c