BBF102E Linear Algebra and Applications Homework Review

A review of linear algebra concepts covered in the lecture for upcoming homework assignments.

To avoid point deductions, ensure solutions begin with __.

The respective questions.

For the unit vectors in the direction of vectors u and v, you must __ them.

Normalize them.

When vectors u and v are perpendicular, their inner product equals __.

Zero.

Two vectors are parallel when the angle between them is __.

Zero degrees.

For the vectors V1, V2, and V3 to be perpendicular, certain conditions on and must be met.

x and y.

A set of vectors is linearly independent if no vector can be expressed as a __ of the others.

Linear combination.

In matrix multiplication, the dot product corresponds to __ of the rows and columns.

Multiplying the elements.

The second row of matrix AB is calculated by __ the corresponding row from A with every column of B.

Multiplying.

A block matrix is symmetric if __ based on its components.

The components are symmetric.

If matrices A and B are symmetric, the resultant matrix AB can be symmetric only under __ conditions.

Specific conditions.