FP1 Flashcards
(42 cards)
The equation ax^2 + bx + c = 0 has roots α and β.
Find (α + β) and αβ.
(α+β) = - b/a
αβ = c/a
What is interval bisection?
Taking the mean m of the interval in which the root lies and test using f(m).
What is linear interpolation?
In linear interpolation we use the method of similar triangles to find the roots of an equation in an interval [a, b].
What is the equation of a circle center (a, b), radius r?
(x-a) ^2 + (y-b) ^2 = r^2
What is the focus of a parabola?
The point that is equidistant from all points on the parabola
What type of roots can a quadratic have?
Real or Complex
What does it mean for a quadratic to have a complex root α?
That the second root β will form a complex conjugate pair with α
What is a complex conjugate?
The complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign
(x-α)(x-β) = 0?
x^2 - (α+β)x + αβ = 0
What is the modulus of a complex number z = a + bi?
√a^2+b^2
What is the argument of a complex number z = a + bi?
tan 𝜃 = b/a (taking correct quadrant into account)
How do complex roots of polynomials occur?
In pairs
How do you know if there is a root in an interval [ a , b ]?
If f(a) and f(b) have different signs
An n x m matrix has…
n rows and m columns
You can matrices if…
They are of same dimension
When multiplying a matrix by a scalar k…
You multiply each element by k
How do you multiply matrices?
You multiply each element in the row of the left hand matrix by the corresponding element in the column of the right hand matrix and adding results together
When can you multiply matrices together?
When the number columns of the left hand matrix is equal to the number of rows of the right hand matrix
When you multiply an n x m matrix with an m x k matrix, the resulting matrix is?
n x k
How can you describe a transformation?
In terms of its effect on the position vector ( x , y )
How can we represent a linear transformation?
Using a matrix
What kinds of transformations are linear?
Rotations, enlargements, reflections
How do you identify the matrix representing a particular transformation?
By considering its effect on i and j.
Given a matrix M, how do identify the transformation it represents?
the columns shows its effect on i and j, this information is used to identify the transformation
