Q1 An identity element leaves other elements _______ when combined with them

A1 unchanged

Q2 the term ______ is often shortened to ‘identity’

A2 identity element

Q3 let (S,*) be a set S with a binary operation * on it. Then an element e of S is called a left identity if _______ for all a in S

A3 e*a=a

Q4 let (S,*) be a set S with a binary operation * on it. Then an element e of S is called a right identity if _______ for all a in S

A4 a*e =a

Q5 let (S,*) be a set S with a binary operation if e*a=a for all a in S and a*e=a for all a in S it is called a two sided identity or simply an ____

A5 identity

Q6 An identity with respect to addition is called an additive identity (often denoted as _____)

A6 0

Q7 An identity with respect to multiplication is called a multiplication identity (often denoted as ____)

A7 1

Q8 There can be several right identities and several left identities but if there is both a left and right then ____

A8 They are equal and there is just a single two sided identity.

Q9 Let (S, *) be a set S with a binary operation * Is it possible for (S,*) to have no identity element .

A9 yes

Q10 Logistic Regression can also handle ____ classification such as 0,1,2,3,4

A10 multiclass

Q11 PyMVPA stands for?

A11 Multivariate Pattern Analysis in Python

Q12 SVM

A12 Support Vector Machine

Q13 The ___ of a linear operator L is the set of all operands v for which L(v) = 0

A13 kernel

Q14 if L:V ->W, ker(L) = {v ∈V:L(v) = 0 } where 0 denotes the null vector in WQ – How do you say this?

A14 The kernel of a linear operator L is the set of all operands v for which L(v)=0

Q15 the kernel of a linear operator R^{m}->R^{n} is the same as the ______ of the correspoding n x m matrix

A15 nullspace

Q16 A collection of linear equations involving the same set of variables.

A16 System of linear equations (or linear system)

Q17 A ____ to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied.

A17 solution

Q18 How do you solve a linear system of two equations

A18 Solve the first equation for x, plug the resulting expression in for x in the second equation -> solve for y -> sub y back in, solve for x

Q19 Term for the number of vectors in a basis.

A19 Its dimension

Q20 The set of all possible solutions for a linear system is called the ______

A20 solution set

Q21 for a linear system involving two variables, each linear equation determines a ______ on the xy-plane

A21 line

Q22 For a linear system involving three variables, each linear equation determines a _____ in 3D space

A22 plane

Q23 For a linear system involving n variables, each linear equation determines a ______ in n-dimensional space

A23 hyperplane

Q24 For a linear system involving n variables, each linear equation determines a hyperplane in _____ space

A24 n-dimensional

Q25 usually, a system with fewer equations than unknowns has _____ solutions

A25 infinitely many

Q26 Usually a system with the same number of equations and unknowns has _____

A26 a single unique solution

Q27 Usually a system with more equations than unknowns has ____

A27 no solution

Q28 The equations of a linear system are ____ if none of the equations can be derived algebraically from the others

A28 independent

Q29 3x + 2y = 6 and 6x + 4y =12 are not _____? They are the same equations when scaled by a factor of two. They would produce identical graphs.

A29 independent

Q30

x-2y=-1

3x+5y=8

4x+3y=7

are not ____ because the third equation is the sum of the other two

A30 independent

Q31 A linear system is ___ if it has a solution and ___ otherwise

A31 consistent, inconsistent

Q32 It is possible for three linear equations to be ____, even though any two of them are consistent together.

A32 inconsistent

Q33 Two linear systems using the same set of variables are ___ if each of the equations in the second system can be derived algebraically from the equations in the first system and vice-versa

A33 equivalent

Q34 f: X->Y – how this read?

A34 f is a function from domain X to codomain Y

Q35 The ___ of a function is the set of all outputs of the function

A35 image

Q36 The image of a function is always a subset of the ___

A36 codomain

Q37 the ____ or target set of a function is the set Y into which all of the output of the function is constrained to fall. It is the set Y in the notation f:X->Y

A37 codomain

Q38 In Category theory, one deals with ____ instead of functions

A38 morphisms

Q39 ____ are arrows from one object to another

A39 morphisms

Q40 The ____ in any morphism is the object from which an arrow starts

A40 domain

Q41 A system of linear equations is considered _____ if there are more equations than unknowns.

A41 overdetermined

Q42 A mapping is invertible if and only if the ____ is non-zero

A42 determinant

Q43 Linear Algebra provides the formal setting for the linear combination of equations used in the ____ ?

A43 Gaussian method

Q44 The ____ method is used to determine the best fit line for a set of data

A44 least squares

Q45 The least squares method will minimize the sum of the squares of the ___

A45 residuals

Q46 An algebraic operation that takes two equal-length sequences of numbers and returns a single number

A46 dot product

Q47 Two non-zero vectors a and b are ___ if and only if a x b = 0

A47 orthogonal

Q48 A function that assigns a strictly positive length or size to each vector in a vector space other than the zero vector

A48 norm

Q49 A vector space on which a norm is defined is called a ____

A49 normed vector space

Q50 The absolute value is a ____ on the real numbers

A50 norm

Q51 Combined with ___ linear algebra facilitates the solution of linear systems of differential equations

A51 calculus

Q52 The study of linear algebra first emerged from the study of _____

A52 determinants

Q53 By ___ a theory of linear transformations of finite-dimensional vector spaces had emerged

A53 1900

Q54 The ____ of a matrix A is denoted det(A), det A, or |A|

determinant

A54 determinant

Q55 The ___ of a matrix is zero if and only if the column vectors (or the row vectors) of the matrix are linearly dependent.

A55 determinant