Math 225 Final Exam Questions with 100% Correct Answers Bundled Package

Heating and Cooling Problems (2.5) Correct Answer Formula: dT/dt = k(M(t) - T(t)), k > 0 (...) General Solution: T(t) = Mo + (To - Mo)e^-kt (...) Problem Conditions: To > Mo = Cooling To < Mo = Heating Exponential Growth and Decay Problems (2.3) Correct Answer Growth: Y(t)...

Linear combination Correct Answer The addition of two or more vectors, each of which can have any weight (scalar). C1v1 + c2v2 + c3v3 Weight Correct Answer The scalar for one of the vectors in a linear combination. Span{v} Correct Answer The set of all vectors of the form cv. Span{v1, v2, ...

G3. Let's first sort out some foundations regarding functions (i.e. transformations). Talk about the following: a. What does the notation

If the columns of A are linearly dependent Correct Answer Then the matrix is not invertible and an eigenvalue is 0 Note that A−1 exists. In order for λ−1 to be an eigenvalue of A−1, there must exist a nonzero x such that Upper A Superscript negative 1 Baseline Bold x equals lambda Superscr...

Augmented matrix Correct Answer a+b=c d+e=f [ a b c ; d e f] Row echelon form (REF) Correct Answer 1. All nonzero rows are above any rows of all zeros, called 0-rows 2. Each leading entry (leftmost nonzero entry) of a row is in a column to the right of the leading entry of the row above it 3....

Elementary row operations Correct Answer 1. (Replacement) Replace one row by the sum of itself and a multiple of another row. 2. (Interchange) Interchange two rows. 3. (Scaling) Multiply all entries in a row by a nonzero constant. X1+x2+x3=2 X2+x3=9 0=-1 This set has ______ solutions and is ...

Span( V1,...,VP) Correct Answer set of all linear combinations Basis of a vector subspace Correct Answer Let H be a subspace of a vector space V. An indexed set B=(v1,...vp) in V is a basis for H if: (i) B is a linearly independent set (ii) the subspace spanned by B coincides with H, that i...