3Blue1Brown Linear Algebra

Question 1

What is a matrix

Answer 1

Transformation of space. Where the basis vectors land

Question 2

Det(M) = 0 means?

Answer 2

The resulting volume of the transformed space is zero

Question 3

Inverse matrix?

Answer 3

Transform is reversed

Question 4

what is dot product?

Answer 4

Answers the question: two vectors: project A onto B, then what is the length of the multiplication of the projection by length of B?

Question 5

two matrices AB; what is the order of operations?

Answer 5

like function composition: f(g(x)) you go from right to left

Question 6

What does Ax=v mean?

Answer 6

The tranformation of A of space causes vector x to land on vector v

Question 7

What is a matrix inverse?

Answer 7

Do the transformation in the opposite direction. A^{-1}

Question 8

When does a matrix inverse not exist?

Answer 8

If the det is 0 that means that the initial transformation squished space. There are infinitely many ways to go in the back direction so the inverse doesn’t exist.

Question 9

What does it mean for a matrix to be full rank?

Answer 9

Rank is the measure of the dimensions of the column space. That is, how many dimensions exist after the transformation. If the same number of dimensions exist, then the matrix is full rank. The matrix is of rank N, where N is the number of dimensions remaining.

Question 10

What are basis vectors?

Answer 10

The unit vectors that define the space.