Linear Algebra Foundations: Vectors and Matrices

Perform vector addition, subtraction, scalar multiplication, and norm computation.

Compute the dot product of two vectors and interpret its geometric meaning.

Perform matrix multiplication and transpose operations.

Describe the concepts of linear independence and span.

Identify the column space and null space of a matrix.

Compute the determinant of a square matrix.

Solve systems of linear equations using matrix operations.

Compute the inverse of an invertible matrix.