Quiz about Wk7 0B2 Review Session MCQs (Matrix Inverses and ODEs)

Question 1

An $$n imes n$$ matrix A is invertible if...

Accepted Answer

a) When going through the Gaussian Elimination process to find an inverse of A you obtain a matrix on the left of an augmented matrix in REF with no zero rows.

Accepted Answer

c) If A represents the left-hand-side (LHS) of equations that has a unique solution.

Answer

b) When going through the process to find an inverse of A you get a row of 1s on the left of an augmented matrix.

Question 2

A differential equation can be (roughly) defined to be...

Accepted Answer

b) an equation that involves derivatives.

Answer

a) an equation.

Answer

c) an equation with two variables.

Answer

d) an integral.

Question 3

Suppose F(x,y) is a function in x and y. What do we mean by "a solution of a differential equation $$\frac{ ext{d}y}{ ext{d}x}=F\left(x,y ight)$$ "?

Accepted Answer

c) A function y(x) such that, when it is substituted into $$\frac{ ext{d}y}{ ext{d}x}=F\left(x,y ight)$$ for y, satisfies the equation.

Answer

a) Numbers for x and y that satisfy the equation.

Answer

b) Another equation in x and y that satisfies the differential equation.

Answer

d) A simplification of the differential equation.

Question 4

Is the following ODE directly integrable

$$\frac{ ext{d}^2y}{ ext{d}x^2}=12x^2$$ ?

Accepted Answer

No

Answer

Yes

Question 5

What is a separable ODE?

Accepted Answer

a) An ODE that we can (re)write as $$\frac{ ext{d}x}{ ext{d}y}=f\left(x ight)g\left(y ight)$$ where $$f\left(x ight)$$ is a function of x only, and $$g\left(y ight)$$ is a function of y only.

Answer

b) An ODE that we can (re)write as $$\frac{ ext{d}x}{ ext{d}y}=f\left(x ight)g\left(y ight)$$ where $$f\left(x ight)$$ is a function of x only.

Answer

c) An ODE that we can (re)write as $$\frac{ ext{d}x}{ ext{d}y}=f\left(x ight)g\left(y ight)$$ where $$g\left(y ight)$$ is a function of y only.

Answer

d) An ODE that we can (re)write as $$\frac{ ext{d}x}{ ext{d}y}=\frac{f\left(x ight)}{g\left(y ight)}$$ where $$f\left(x ight)$$ is a function of x only, and $$g\left(y ight)$$ is a function of y only.

Question 6

What do we mean by a linear (first order) ODE.

Accepted Answer

d) An ODE that can be written in the form $$\frac{ ext{d}y}{ ext{d}x}+P\left(x ight)y=Q\left(x ight)$$ where P(x) and Q(x) are functions in x only.

Answer

a) A differential equation that can be written in the form y=mx+c, for some constants m and c.

Answer

b) An ODE that can be written in the form $$\frac{ ext{d}y}{ ext{d}x}=F\left(x,y ight)$$ where F(x,y) is a linear function.

Answer

c) An ODE that can be written in the form $$\frac{ ext{d}y}{ ext{d}x}+P\left(x ight)y=Q\left(x ight)$$ where P(x) and Q(x) are linear functions in x only.

Question 7

What is an integrating factor of the ODE $$\frac{dy}{dx}+\frac{y}{x-1}=x+1$$ ?

Accepted Answer

b) x-1

Answer

a) $$e^{x-1}$$

Answer

c) $$\ln\left|x-1\right|$$

Answer

d) $$x+1$$

Question 8

What do we do with an integrating factor (IF) to solve an ODE?

Accepted Answer

c) Multiply the both sides of the ODE by the IF.

Answer

a) Multiply the LHS of the ODE by the IF.

Answer

b) Multiply the RHS of the ODE by the IF.

Answer

d) Multiply the IF by the ODE.

Wk7 0B2 Review Session MCQs (Matrix Inverses and ODEs)

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