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MATH 290-1 Midterm 1
Matrices
20
Mathematics
Undergraduate 1
10/18/2011

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Cards

Term
Standard Matrix to Reflect over x-axis
Definition

[1  0]

[0 -1]

Term
Standard Matrix to Reflect over y-axis
Definition

[-1 0]

[0  1]

Term
Standard Matrix to Reflect over y=x
Definition

[0 1]

[1 0]

Term
Standard Matrix to Reflect over y=-x
Definition

[0  -1]

[-1  0]

Term
Standard Matrix for Horizontal Scaling
Definition

[k  0]

[0  1]

Term
Standard Matrix to Reflect over Origin
Definition

[-1  0]

[0  -1]

Term
Standard Matrix for Vertical Scaling
Definition

[1  0]

[0  k]

Term
Standard Matrix for Horizontal Shear
Definition

[1  k]

[0  1]

Term
Standard Matrix for Vertical Shear
Definition

[1  0]

[k  1]

Term
Standard Matrix to Project on x-axis
Definition

[1  0]

[0  0]

Term
Standard Matrix to Project on y-axis
Definition

[0  0]

[0  1]

Term
When is T one-to-one?
Definition
When columns of A are linearly independent
Term
For T to map Rn onto Rm...
Definition
A must span Rm
Term
Theorem 4
Definition

1. Ax = b always has solution

2. each b is linear combination of A

3. Columns of A span Rm

4. A has pivot in every row

 

all true or none true

Term
For T to be onto...
Definition
T(x) = b has at least one solution
Term
Trivial Solution
Definition
only solution is zero vector
Term
Domain
Definition
Set of Vectors that can be evaluated (Rn)
Term
Codomain
Definition
Space Containing Output (Rm)
Term
Image
Definition
If x is in domain of f:Rn -> Rm then f(x) is image
Term
Range
Definition
set of vectors in codomain which are image of something in domain
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