Exam (elaborations)
Math 218 Midterm Questions And Answers Latest Update
- Course
- Math 218
- Institution
- Duke University
Math 218 Midterm Questions And Answers Latest Update
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Solution 2024/2025Pepper
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)
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