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MATH 136 - WINTER 2019 - UWATERLOO - THEOREMS AND DEFINITIONS
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MATH 136 - WINTER 2019 - UWATERLOO - THEOREMS AND DEFINITIONS
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MATH 136 - WINTER 2019 - UWATERLOO -THEOREMS AND DEFINITIONS
- ANS-Define: Linear Combination
- ANS-Define: Span
- ANS-Some vector in a set can be written as a linear combination of the others in the set.......
- ANS-Define linearly dependent and linearly independent
- ANS-A set of vectors is linearly dependent if and only if....
It is linearly dependent - ANS-If a set of vectors contains the zero vector.....
- ANS-Define what a basis is
- ANS-Define what the standard basis is
- ANS-What is a line ?
- ANS-What is a plane?
- ANS-What is a hyperplane?
- ANS-Define k-flat
- ANS-What is the subspace test?
- ANS-Give properties of the dot product
- ANS-What is the formula for cross product?
- ANS-Give properties of the cross product
- ANS-Give the equation of plane in 3-space two ways
- ANS-Give the scalar equation of a hyperplane
- ANS-Give the formula for projection/perpendicular onto a line
, - ANS-Give the formula for projection/perpendicular onto a plane
- ANS-Define the following: consistent system, inconsistent system, solution of a system
- ANS-If the a system of m equations in in n variables has two distinct solutions then.....
- ANS-State the three ERO's and what it means to be row equivalent
1) All rows containing a non-zero entry are above those only containing zeros
2)The first non-zero entry in each non-zero row is a 1, called a leading one
3) The leading one is each non-zero row is to the right of the leading one in any row above it
4) A leading one is the only non-zero entry in its column - ANS-State what it means for a matrix
to be in RREF
- ANS-What is a free variable?
- ANS-What is a homogeneous system? What is the solution set of a homogeneous system
called?
- ANS-What is rank? For any m x n matrix rank .....
- ANS-State the System-Rank Theorem
- ANS-State the Solution Theorem
- ANS-What is the transpose of a matrix? State properties of transpose
- ANS-What are the two ways to do matrix-vector multiplication?
- ANS-Define matrix multiplication. For it to be defined, what must be true in terms of sizes of
the matrices
- ANS-State the properties of matrix multiplication
- ANS-Define what it means for a function to be a linear mapping
- ANS-State the Matrices Equal Theorem
- ANS-What is the identity matrix?
- ANS-What is the rotation matrix? What is a reflection?
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