Linear Algebra Test 2

"What is a matrix?"

"A box of numbers that helps us do math like a grid of values."

"What is an inverse matrix?"

"A special matrix that undoes what another matrix does."

"What is the identity matrix?"

"A matrix that keeps things the same when you multiply by it

"What is the column space?"

"All the possible results you can get when you multiply the matrix by different vectors."

"What is the null space?"

"All the secret vectors that turn into zero when multiplied by the matrix."

"What is a subspace?"

"A smaller space inside a bigger space that follows the same math rules."

"What does 'span' mean?"

"All the things you can make by mixing certain vectors together

"What is a basis?"

"The smallest set of vectors that can build everything in a space

"What is dimension?"

"The number of directions or building blocks needed to make a space."

"What is rank?"

"How many directions a matrix can move you in — how much it can do."

"What is nullity?"

"How many invisible vectors turn into zero when multiplied by the matrix."

"What is the Rank–Nullity Theorem?"

"It says rank plus nullity equals the total number of columns in a matrix."

"What is a linear transformation?"

"A math machine that turns one vector into another without breaking the rules of addition or scaling."

"What is the kernel of a transformation?"

"All the vectors that get turned into zero by the transformation."

"What is the range of a transformation?"

"All the possible outputs the transformation can make."

"What does 'one-to-one' mean?"

"Each input makes a unique output — no two things look the same at the end."

"What does 'onto' mean?"

"The transformation can reach every possible output in the space."

"What does it mean for a matrix to be invertible?"

"It can undo itself — you can go backward or forward perfectly."