Math 218 Midterm Exam with Questions and Answers
square matrix ANSWER an m x n matrix is square if m = n
the diagonal of a matrix ANSWER refers to the collection of (i,i) entries of the matrix
upper triangular ANSWER refers to a matrix if every entry below the diagonal is zero
lower tri...
Math 218 Midterm Exam with Questions
and Answers
square matrix ANSWER an m x n matrix is square if m = n
the diagonal of a matrix ANSWER refers to the collection of (i,i) entries of the matrix
upper triangular ANSWER refers to a matrix if every entry below the diagonal is zero
lower triangular ANSWER refers to a matrix if every entry above the diagonal is zero
diagonal ANSWER refers to a matrix if every non diagonal entry is zero
diag(d1, .... dn) ANSWER is the n x n diagonal matrix w/ the diagonal d1, ... dn (everything
else is 0)
zero vector, zero matrix ANSWER vector or matrix that are full of zeros. can write O2 or
O4x3 for ex. (doesnt have to be square)
nonzero ANSWER a matrix or vector if at least one entry is nonzero
In ANSWER the n x n identity matrix which has ones on the diagonal and zeros everywhere
else
first pivot column ANSWER first non-zero column
rank one ANSWER every column is a multiple of the first pivot column
, vecotr in R^n ANSWER is a list of n coordinates organized vertically in a list
matrix m x n ANSWER R^(m x n)
scalar v product ANSWER vector w. scalar multiplied by each coordinate
vector addition ANSWER add up coordinates across the rows
scalar matrix products ANSWER multiply scalar by every coordinate in the matrix
matrix addition ANSWER add up coordinates with the same position. onlt matrices of the
SAME SHAPE can be added togehter
A^T ANSWER formed by interchanging rows and columns
transposition is ANSWER a linear operation meaning it can be distributed. so, (c1A1 +
c2A2)^T = c1At + csAt)
symmetric ANSWER sT = S, symmetry across the diagonal
trace(matrix) ANSWER 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 ANSWER gives you a vector, in the form: scalar1*v1 +
scalar2*v2...+snvn
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