|Stony Brook University
||Introduction to Linear Algebra
Check list for Midterm I
- How to solve a system of linear equations using Gauss-Jordan elimination?
- What is the redused row-echelon form (rref) of a matrix, how to find it, and how the
rref of a matrix gives the solution of a linear system?
- What is the rank of a matrix?
- How does the solution of a linear system depend on the ranks of coefficient-
and augmented matrices?
- How to add and multiply matrices?
- Matrix multiplication is accociative, but not commutative!
- What is a vector? How to add vectors and take a scalar multiple of a vector? Which vectors
- What is Rn? Who lives there? What can we do with
- How to calculate the dot product of two vectors in Rn. What is the norn of a vector?
- What does it mean that two vectors are orthogonal?
- What is a linear transformation? Can you give some examples?
- What is the matrix of a linear transformation and how to find it?
- Linear transformations on a plane: scaling, projection, reflection, rotation,
- What is a composition of linear transformations and how to find its matrix?
- What is the inverse thansformation?
- An isomorphism is an invertible linear transformation.
- What is the inverse matrix?
- How to invert a matrix?
- What is a subspace of Rn?
- What is a linear combination of vectors?
- What is a span of vectors?
- Which vectors are said to be linearly dependent?
- Which vectors are said to be linearly independent?
- How to test linear dependence/independence?
- What is the kernel of a linear transformation?
- What is the image of a linear transformation?
- What does it mean that vectors form a basis of a subspace?
- What is the dimension of a subspace?
- What does the Kernel-Image (Rank-Nullity) theorem say?
- Can you say "A matrix is invertible" in nine different ways?
- The rank of a matrix is the dimension of the image.
- What are coordinates of a vector with respect to a basis?
- How to find a matrix of a linear transformation with respect to some basis?
- What is a relation between matrices of a linear map with respect to two different bases?
- Which matrices are called similar?