Linear Algebra & Multivariable Calc Quiz

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Key concepts review

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Froggy Jumps Linear Algebra & Multivariable Calc QuizVersión en línea Key concepts review por Tyler Larson 1 What equation do you solve to find eigenvalues of A? a det(A) = λI - Iλ b det(A + λI) = 0 c det(A - λI) = 0 2 What is the set of all eigenvectors for a given λ called? a Nullspace b Eigenspace c Span of A's columns 3 A matrix is diagonalizable if the sum of geometric multiplicities equals what? a The number of distinct eigenvalues b The rank of A c n 4 How are derivatives of a vector-valued function r(t) computed? a As a single scalar derivative b Component-wise c Only by Jacobians 5 What is the tangent line to r(t0) in vector form? a L(u) = r(t0) + u r'(t0) b L(u) = r(t0) - u r'(t0) c L(u) = r'(t0) 6 Which formula gives arc length of a curve? a L = \|r(b) - r(a)\| b L = ∫_a^b \|r'(t)\| dt c L = ∫_a^b r(t) dt 7 Curvature uses which components of motion? a T and a (tangent and acceleration) b Normal force and tension c Speed only 8 Clairaut’s theorem concerns equality of which derivatives? a f_xx and f_yy b First derivatives only c f_xy and f_yx 9 What does a level curve represent for f(x,y)? a Points where f is maximal b Points where f(x,y) = c c Points where ∇f = 0 10 Path dependence shows a limit does not exist by what method? a Using two different paths b Using a single path c Changing the function definition

Froggy Jumps

Linear Algebra & Multivariable Calc QuizVersión en línea

Key concepts review

por Tyler Larson

What equation do you solve to find eigenvalues of A?

det(A) = λI - Iλ

det(A + λI) = 0

det(A - λI) = 0

What is the set of all eigenvectors for a given λ called?

Nullspace

Eigenspace

Span of A's columns

A matrix is diagonalizable if the sum of geometric multiplicities equals what?

The number of distinct eigenvalues

The rank of A

How are derivatives of a vector-valued function r(t) computed?

As a single scalar derivative

Component-wise

Only by Jacobians

What is the tangent line to r(t0) in vector form?

L(u) = r(t0) + u r'(t0)

L(u) = r(t0) - u r'(t0)

L(u) = r'(t0)

Which formula gives arc length of a curve?

L = |r(b) - r(a)|

L = ∫_a^b |r'(t)| dt

L = ∫_a^b r(t) dt

Curvature uses which components of motion?

T and a (tangent and acceleration)

Normal force and tension

Speed only

Clairaut’s theorem concerns equality of which derivatives?

f_xx and f_yy

First derivatives only

f_xy and f_yx

What does a level curve represent for f(x,y)?

Points where f is maximal

Points where f(x,y) = c

Points where ∇f = 0

Path dependence shows a limit does not exist by what method?

Using two different paths

Using a single path

Changing the function definition

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Linear Algebra & Multivariable Calc Quiz

Froggy Jumps

Sobre esta actividad

Creada por

Descarga la versión para jugar en papel

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Linear Algebra & Multivariable Calc QuizVersión en línea

por Tyler Larson

What equation do you solve to find eigenvalues of A?

What is the set of all eigenvectors for a given λ called?

A matrix is diagonalizable if the sum of geometric multiplicities equals what?

How are derivatives of a vector-valued function r(t) computed?

What is the tangent line to r(t0) in vector form?

Which formula gives arc length of a curve?

Curvature uses which components of motion?

Clairaut’s theorem concerns equality of which derivatives?

What does a level curve represent for f(x,y)?

Path dependence shows a limit does not exist by what method?

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