1) Let Vector V = (5,5) ad Vector U = (3,4). What is the length of the projected vector proj_UV?

2) If a projected vector proj_UV = 0, then vectors U and V must be?

Answer Choices: Parallel to each other

At an obtuse Angle

Perpendicular to each other

3) In Linear Regression, can the norm of the fitted vector y* be larger than the norm of the observed response Vector Y? (Hint: think about the geometry of orthogonal projection)

Answer choices: Always, Sometimes or Never

4) If a linear regression has an intercept term, then the norm of the residual vector E must be 0?

Answer choices: Yes or No

5) Is the function T: R² --> R defined by the T(x,y) = xy a linear transformation?

Answer choices: Yes or No

6) Is the function T: R² --> R defined by the T(x,y) = 3x-5y a linear transformation?

Answer choices: Yes or No

7) What kind of transformation does a diagonal matrix A do?

Answer Choices: Projection

Rotation

Scaling Coordinates

Shear

8) Can an orthogonal matrix Q change the norm of a Vector V when multiplying with it?

Answer Choices: Always, Sometimes, or Never