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1. Linear Algebra

2. Sachin Mittal

Co-founder and Instructor at GO Classes
MTech IISc Bangalore

Ex Amazon Applied Scientist

GATE AIR 33

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3. Linear Algebra

4. Why study linear algebra ?

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From Data to Vectors and Matrices

9. Linear Algebra is fuel of machine learning...

10. Why Study Linear Algebra ?

Linear Algebra is fuel of machine learning...

Every Type of data can be represented as matrices or as vectors.

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16. Recommendation Engines — Making use of embeddings

+ Different types of users -
kids, adults, teenagers, etc.

«Ratings of movies.
+ Types of movies.

«Movies for kids and for adults.

Source: Google's Machine Learning course on Recommendation Systems

17. Industries where Linear Algebra is used heavily

+ Statistics

* Chemical Physics

* Genomics

+ Word Embeddings — neural networks/deep learning
* Robotics ——

« Image Processing ——

* Quantum Physics

18. Linear Algebra for GATE

1-2 Gusto weil gear

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19. 24 GATE CSE 2023 | Question: 20
MES] Let A be the adjacency matrix of the graph with vertices (1, 2, 3, 4, 5}. Let
#1 A1, A2,A3, Aa, and À; be the five eigenvalues of A. Note that these
eigenvalues need not be distinct. The value of A; + A2 + Az + Ag +; =

34 GATE CSE 2023 | Question: 8

En tet
#2
1234
aa 2 8
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25 2 à GATE 2822

and \[ B=\left{\begin{array}{llil} 3 8 4 & ... det(B) = — det(A) det(A) = 0
det(AB) = det(A) + det(B)

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23. © SAKSHI JOSHI FEATURED REVIEW x 1200
MORA A E months ago

For the first time, | actually understood what exactly is linear algebra, whenever I study linear algebra itjust seems like a lot of processes and formulas
but after attending Sachin sir classes all the formulas and process now seems logical and instead of memorizing everything | am able to understand and
apply the concepts .it was just very satisfying. Sachin sir explain the system of linear equations with so much clarity now | am able to decode and answer

GATE questions with ease. Thank you go classes for providing such an awesome course!

- Sakshi Joshi (IITM)

24. MILIN BHADE FEATURED REVIEW

| really enjoyed the course. It helped me so much inlinte after G was confident to answer question

- Milin Bhade (IISc)

=

25. HARSH VISHWAKARMA

o allt ing these re q o register for the course, just do it! The

ing style is fi we feeling tudying mathematic mputer S

- Harsh (IISc)
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27. SRIDHAR BAJPAI FEATURED REVIEW

ır problem solving ability. just blindly follow course content cont

Sridhar (AIR 25, IISc)

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28. P} PK FEATURED REVIEW

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watching the le me to know that | was byhea

ing a lot of formulaes, | also ca know what real
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maths which | never knew existed from the applications of Linear All
probability that information. It was tremendous :-) and helped me se
any further Al specialised exams and|ntery

29. FM ABHISHEK SOLANKI + ‘st 5
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| am very delighted to share that I will be j
in Computation And Data Science(CDS).

ing IISc Bangalore for my M-Tech
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| would like to thank Ankit Ahirwar ‚Adesh Tiwari for helping me throughout

my journey and completing my college assignments and for marking my

proxies so that | can give my whole time for GATE prepration. am thankful to
¡ave you guys.

sre Ga cite eh eka at Ge el A ET ete!

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I would like to thank Sachin Mittal sir, and GATE Overflow for the precious

guidance , and for helping me in cracking interviews of IISc Bangalore and IIT

Delhi. ———
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Thankyou sachin sir once again. —
This couldn't be possible without you. A À

30. aditya al
last seen recently

Hello sir
| got selected in IIT Kanpur MS winter admissions

| watched your linear algebra and probability course and almost

all the interview questions were asked from what you taught
sa

| want to say a big thank you to you and go classes for providing
these lectures

Aditya (IITK)

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42. Scalar times vector

43. Vector addition

44. Vector addition

45. Linear Combination of vectors

46. Linear Combination of vectors

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55. This gentle introduction ta and voor Doms
simple, but you may be surpri to learn that nearly
all of linear algebra is built up from scalars and vectors.
From humble beginnings, amazing things emerge. Just
think of everything you can build with wood planks and
nails. (But don’t think of what J could build — I’ma
terrible carpenter.)

56. Linearly Dependent vectors

57. Linearly Dependent vectors

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61. One important thing to know about linear independence before
reading the rest of this section is that independence is a prop-
erty of a set of vectors. That is, a set of vectors can be linearly
independent or linearly dependent; it doesn’t make sense to ask
whether a single vector, or a vector within a set, is independent.

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81. Linear Dependence

* At least one vector can be obtained by linear combination of other
vectors
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* If we can obtain zero vector by nontrivial (atleast one c; is non-zero)
linear combination of other vectors
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A. If (uy, U2, uz) is linearly dependent, so is {u1, >}.

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B. If u, is not a linear combination of {u1, uz, uz], then {u1, u2, uz, ua} is linearly
independent.

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99. (c) TRUE or FALSE: If (u;, us, us} is linearly dependent, so is {u1, uz.)

0 L 0
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0 0 0

which you can take out the zero vector and end up with two linear
independent vectors.

100. (d) TRUE or FALSE: If uy is not a linear combination of (u;, uz, uz),
then {uy, ug, uz, us) is linearly independent.
This is false: Any one of the other vectors could be the zero vector, for

example.

101. Linear Independence

102. Linear Independence

a set of vectors is said to be linearly independent

* If we can obtain zero vector only by trivial linear combination of other vectors
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