Matrices + Vectors Flashcards
How do you multiply matrices?
How do you find the inverse of a 2x2 matrix?
What is the feature of the inverse of a matrix?
How do you find the inverse of a matrix?
How do you find adj(A)?
How do you find the unit vector?
How do you find the normal of a plane using two unit vectors?
What is the cross product rule?
What is the equation of a traingle?
How do you multiply vectors?
How do you calculate eigenvalues?
How do you calculate eigenvectors?
How do you find the intersection of a point and a line?
How do you find the smallest distance between a point and a line?
How do you find the intersection of two lines?
How do you find the distance between two lines?
Equation given in book.
Remember a x b does not equal a · b!
Work a x b out first and then just insert this value into the equation. You can also find |a x b| from this which is again inserted into equation!
How do you find the angle between two lines?
How do you find the distance between a point and a plane?
How do you find the angle between a point and a plane?
How do you find the intersection of two planes?
How do you find the distance between two planes?
How do you find the angle between two planes?
How do you find the transformation matrix for image points?
How do you find the image of a point?
Hows do you find the image of a transformed plane?
How do you set up simultaneous equations using matrices and vectors?
How do you perform Gaussian elimination to solve simultaneous equations?
What is the quadratic formula?
How do you complete force problems?
- Calculate the unit direction vectors in which you need to find the force.
- Calculate the force direction unit vector.
- Calculate the force vector by multiplying the unit vector by the magnitude of force.
- Use the dot product between the force vector and each unit direction vector in order to find the force in that direction.
How to model mass-spring systems
How do you find inclined asymptotes?
- If numerator has higher power then denominator:
Divide numerator by denominator to find equation for asymptote.
- If denominator has higher power then numerator:
There is a horizontal asymptote at y=0.
- If numerator and denominator both have same maximum power:
Take the coefficients of these maximum powers and divide.
3x2 + x = 3 = 3
x2 +1 1
How do you find the volume of revolution of a 3D shape?
If the curve of the shape is constant the throughout (such as a bowl) you can ignore the one plane and set to zero (for example y = 0.
You can then use the equations to solve as normal.
Watch for upper and lower values.
If symmetrical, pick one side of the axis as this will revolve 360 degrees around axis and give no overlap.
