100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Math 218 Midterm Questions And Answers Latest Update $14.49   Add to cart

Exam (elaborations)

Math 218 Midterm Questions And Answers Latest Update

 7 views  0 purchase

Math 218 Midterm Questions And Answers Latest Update

Preview 3 out of 16  pages

  • November 1, 2024
  • 16
  • 2024/2025
  • Exam (elaborations)
  • Questions & answers
All documents for this subject (8)
avatar-seller
Schoolflix
Solution 2024/2025
Pepper

Math 218 Midterm Questions And Answers
Latest Update

square matrix ANS✔✔ an m x n matrix is square if m = n



the diagonal of a matrix ANS✔✔ refers to the collection of (i,i) entries of the
matrix



upper triangular ANS✔✔ refers to a matrix if every entry below the diagonal
is zero



lower triangular ANS✔✔ refers to a matrix if every entry above the diagonal
is zero



diagonal ANS✔✔ refers to a matrix if every non diagonal entry is zero



diag(d1, .... dn) ANS✔✔ is the n x n diagonal matrix w/ the diagonal d1, ...
dn (everything else is 0)



zero vector, zero matrix ANS✔✔ vector or matrix that are full of zeros. can
write O2 or O4x3 for ex. (doesnt have to be square)



nonzero ANS✔✔ a matrix or vector if at least one entry is nonzero

, Solution 2024/2025
Pepper
In ANS✔✔ the n x n identity matrix which has ones on the diagonal and
zeros everywhere else



first pivot column ANS✔✔ first non-zero column



rank one ANS✔✔ every column is a multiple of the first pivot column



vecotr in R^n ANS✔✔ is a list of n coordinates organized vertically in a list



matrix m x n ANS✔✔ R^(m x n)



scalar v product ANS✔✔ vector w. scalar multiplied by each coordinate



vector addition ANS✔✔ add up coordinates across the rows



scalar matrix products ANS✔✔ multiply scalar by every coordinate in the
matrix



matrix addition ANS✔✔ add up coordinates with the same position. onlt
matrices of the SAME SHAPE can be added togehter



A^T ANS✔✔ formed by interchanging rows and columns



transposition is ANS✔✔ a linear operation meaning it can be distributed. so,
(c1A1 + c2A2)^T = c1At + csAt)

, Solution 2024/2025
Pepper



symmetric ANS✔✔ sT = S, symmetry across the diagonal



trace(matrix) ANS✔✔ the sum of its diagonal, matrix must be square, is a
scalar, is a linear operation (can be distributed and can take the scalar out)



linear combination ANS✔✔ gives you a vector, in the form: scalar1*v1 +
scalar2*v2...+snvn



matrix-vector products ANS✔✔ encoded linear combinations, matrix holds
vectors and scalars go into v. vector can also be used to add and subtract
some of the columns, warning #collumns A must = #rows v!!)



3 matrix-vector multiplication rules ANS✔✔ linearity, identity, and zero rules



linearity rule ANS✔✔ A(c1v1 + c2v2) = c1Av1 + c2Av2 (matrix x vector,
order matters)



identity rule ANS✔✔ Inv = v



zero rule ANS✔✔ A0n = 0m ,0n is vector, 0m is vector:)



R^n --A--> R^m ANS✔✔ sophisticated way of writing A is m x n matrix (not
order of rows and columns changes)

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller Schoolflix. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $14.49. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

73216 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$14.49
  • (0)
  Add to cart