Vector Spaces III Lowersixth Science Further Mathematics

Froggy Jumps

Jugadas 0

Crear copia

Sobre esta actividad

Core concepts for vectors, spaces, and transformations.

Creada por

YAKILI LMS

Camerún

Descarga la versión para jugar en papel

Crea tu propio juego gratis desde nuestro creador de juegos

Compite contra tus amigos para ver quien consigue la mejor puntuación en esta actividad

Crear reto

OPEN UP 6 UNIT 1 VOCABULARY

karen blixen

España

(98)

Repasamos el vocabulario de la unidad
El valle de los lobos

Marcos Signes

España

(107)

20 preguntas de este maravilloso libro
Quiz de Culpa mía película

Yamila Chavez

Argentina

(170)

Demuestra cuánto sabes sobre la película Culpa mía con este divertido quiz.
Salva a la Ranita

Melanie Rodriguez

Estados Unidos

(335)

Contesta las siguientes multiplicaciones correctamente para salvar a la ranita y evitar que caiga al agua, mucha suerte!
Sabiduría animal

Educaplay Educational Resources

España

(15379)

Conviértete en un genio del Reino Animal

		%
	Anónimo	%
		%
		%

Imprime tu juego

Vector Spaces III Lowersixth Science Further Mathematics


Froggy Jumps Vector Spaces III Lowersixth Science Further MathematicsVersión en línea Core concepts for vectors, spaces, and transformations. por YAKILI LMS 1 What defines linear dependence among vectors? a All vectors are zero b All vectors are equal c A nontrivial combination equals zero 2 What is a basis of a vector space? a A set of independent vectors spanning the space b A set of vectors with a common direction c A single vector that repeats 3 What is the dimension of a vector space? a Number of vectors in a basis b Largest eigenvalue c Number of vectors in the space 4 If v1, v2 are independent, what is their span? a All linear combinations of v1 and v2 b Only v1 and v2 themselves c Only zero vector 5 What is a linear transformation? a A map preserving addition and scalar multiplication b A map that inverts vectors c A map preserving only addition 6 Matrix of a linear transformation depends on what? a The determinant only b The dimension only c Choice of basis for domain and codomain 7 What does the matrix A represent in T(x) = Ax? a The inverse transformation b The eigenvector c The linear transformation relative to bases 8 Eigenvalues satisfy what equation? a Det(A) = 0 b Aλ = I c Det(A - λI) = 0 9 Eigenvectors correspond to which relation? a Av = λv for some nonzero v b Av = v c Av = 0 for all v 10 What is an eigenvector of a matrix A? a A nonzero vector v with Av = λv b A vector with determinant 1 c Any vector mapped to zero 11 How many eigenvalues can a 2x2 matrix have (counting multiplicity)? a Infinite b Two c One 12 If A is diagonalizable, what can be said about A? a A has zero determinant b A is always symmetric c There exists a P such that P^{-1}AP is diagonal 13 What is the eigenvector for a multiple of the identity matrix I? a Only the zero vector b Only vectors perpendicular to I c Any nonzero vector 14 What does the trace of A equal when A has eigenvalues λ1, λ2? a Sum of eigenvalues b Determinant of A c Product of eigenvalues 15 If v is an eigenvector for eigenvalue λ, what is Av? a v/λ b Av = v c λv 16 What is the null space of a matrix A? a Set of eigenvectors only b Set of x with Ax = 0 c Set of x with Ax = x 17 Rank-Nullity Theorem relates to what? a Trace equals nullity b Dimension of domain = rank(A) + nullity(A) c Determinant equals rank 18 What is a linear transformation’s kernel? a Set of vectors mapped to zero b Set of vectors mapped to identity c Set of eigenvectors 19 What is a linear transformation’s image? a Determinant of T b Set of all outputs T(v) c Set of all inputs v 20 What does a 3x3 matrix represent in R^3? a A scalar function b A vector in R^3 c A linear map from R^3 to R^3 21 Which operation preserves linear independence? a Multiplying by zero b Adding dependent vectors c Applying an invertible matrix 22 What is a basis for R^2? a One vector b Two independent vectors in R^2 c Three dependent vectors 23 What is the dimension of span{e1, e2} in R^2? a 2 b 1 c 3 24 What is a column space? a Span of the matrix columns b Span of the rows c The null space itself 25 If columns of A are dependent, what is rank(A)? a Equal to number of columns b Zero c Less than number of columns 26 Eigenvectors corresponding to distinct eigenvalues are a Zero b Linearly independent c Identical 27 What is a diagonal matrix D? a Only diagonal entries nonzero b Nonzero off-diagonal entries c All zeros only 28 What does eigenvalue decomposition require? a A is symmetric only b A is singular c A is diagonalizable 29 What is a nullity of A? a Sum of eigenvalues b Dimension of row space c Dimension of the null space 30 A linear transformation preserves a Distance only b Angle only c Vector addition and scalar multiplication 31 Which set is a subspace? a Any subset of vectors b Nonempty, closed under addition and scalar mult c Only the zero vector 32 What is the image of a basis under a linear map? a Always the zero vector b Always equal to input c The set of their images spanning the target 33 What is the determinant zero indicating? a Matrix is singular b Matrix is diagonal c Matrix invertible 34 What is a similarity transformation? a Transposing A only b P^{-1}AP = B for some A,B c A new matrix equal to A 35 What is the characteristic polynomial? a Trace(A) - λ b Det(A + λI) c Det(A - λI) 36 What can you say about eigenvectors of a triangular matrix? a Eigenvectors are on diagonal b Eigenvalues are on the diagonal c No eigenvalues exist 37 How do you test independence of a set? a See if they are all equal b Check length only c Solve c1v1 + c2v2 + ... = 0 38 What is a homogeneous system? a Right-hand side equals identity b All constant terms are zero c All variables are zero 39 What does a basis enable you to do? a Represent any vector uniquely b Create zero vectors only c Change dimension arbitrarily 40 What is the rank of a zero matrix? a n b 1 c 0 41 What is a linear transformation’s matrix relative to bases? a Determinant only b Matrix representation mapping coordinates c Scalar value 42 What does a full rank imply? a Independent columns equal dimension b Dependent columns c Zero determinant 43 What is the eigenvector condition for A in R^n? a Av = 0 for all v b Av = λv for some λ c Av = v 44 What is a linear combination? a Product of vectors b Sum of scalars times vectors c Difference of vectors 45 What is the image of the standard basis under a map? a The rows of the map b The column vectors of the map c Always zero 46 What is an invariant subspace? a Only zero vector b Mapped to itself under T c Mapped outside itself 47 What is a linear independence test? a Nontrivial combination equals zero b All coefficients equal one c Only trivial combination equals zero 48 What is a 2x2 eigenvalue problem example? a Solve Av = I b Compute A^2 = I c Solve det(A - λI) = 0 49 What is a basic property of eigenvectors for distinct λ? a They must be orthogonal b They are identical c They are linearly independent 50 What does diagonalization require? a A has enough eigenvectors to form a basis b Matrix must be symmetric only c Determinant must be zero

Vector Spaces III Lowersixth Science Further Mathematics

Froggy Jumps

Sobre esta actividad

Creada por

Descarga la versión para jugar en papel

Top juegos

Froggy Jumps

OPEN UP 6 UNIT 1 VOCABULARY

Froggy Jumps

El valle de los lobos

Froggy Jumps

Quiz de Culpa mía película

Froggy Jumps

Salva a la Ranita

Froggy Jumps

Sabiduría animal

Froggy Jumps

Vector Spaces III Lowersixth Science Further MathematicsVersión en línea

por YAKILI LMS

What defines linear dependence among vectors?

What is a basis of a vector space?

What is the dimension of a vector space?

If v1, v2 are independent, what is their span?

What is a linear transformation?

Matrix of a linear transformation depends on what?

What does the matrix A represent in T(x) = Ax?

Eigenvalues satisfy what equation?

Eigenvectors correspond to which relation?

What is an eigenvector of a matrix A?

How many eigenvalues can a 2x2 matrix have (counting multiplicity)?

If A is diagonalizable, what can be said about A?

What is the eigenvector for a multiple of the identity matrix I?

What does the trace of A equal when A has eigenvalues λ1, λ2?

If v is an eigenvector for eigenvalue λ, what is Av?

What is the null space of a matrix A?

Rank-Nullity Theorem relates to what?

What is a linear transformation’s kernel?

What is a linear transformation’s image?

What does a 3x3 matrix represent in R^3?

Which operation preserves linear independence?

What is a basis for R^2?

What is the dimension of span{e1, e2} in R^2?

What is a column space?

If columns of A are dependent, what is rank(A)?

Eigenvectors corresponding to distinct eigenvalues are

What is a diagonal matrix D?

What does eigenvalue decomposition require?

What is a nullity of A?

A linear transformation preserves

Which set is a subspace?

What is the image of a basis under a linear map?

What is the determinant zero indicating?

What is a similarity transformation?

What is the characteristic polynomial?

What can you say about eigenvectors of a triangular matrix?

How do you test independence of a set?

What is a homogeneous system?

What does a basis enable you to do?

What is the rank of a zero matrix?

What is a linear transformation’s matrix relative to bases?

What does a full rank imply?

What is the eigenvector condition for A in R^n?

What is a linear combination?

What is the image of the standard basis under a map?

What is an invariant subspace?

What is a linear independence test?

What is a 2x2 eigenvalue problem example?

What is a basic property of eigenvectors for distinct λ?

What does diagonalization require?