1. Let a,b,c,d be row vectors and form the matrix A whose rows
are a,b,c,d. If...
1. Let a,b,c,d be row vectors and form the matrix A whose rows
are a,b,c,d. If by a sequence of row operations applied to A we
reach a matrix whose last row is 0 (all entries are 0) then:
a. a,b,c,d are linearly dependent
b. one of a,b,c,d must be 0.
c. {a,b,c,d} is linearly independent.
d. {a,b,c,d} is a basis.
2. Suppose a, b, c, d are vectors in R4 . Then they form a...
Let M be an n x n matrix with each entry equal to either 0 or...
Let M be an n x n matrix with each entry equal to either 0 or 1.
Let mij denote the entry in row i and column j. A
diagonal entry is one of the form mii for some i.
Swapping rows i and j of the matrix M denotes the following
action: we swap the values mik and mjk for k
= 1,2, ... , n. Swapping two columns is defined analogously.
We say that M is rearrangeable if...
(1 point) Consider the linear code
?={000000,001011,010101,011110,100110,101101,110011,111000}.
(a) Find a generator matrix for ?.
(b) Find...
(1 point) Consider the linear code
?={000000,001011,010101,011110,100110,101101,110011,111000}.
(a) Find a generator matrix for ?.
(b) Find a check matrix for ?.
Consider the following two ordered bases of R^2:
B={〈1,−1〉,〈2,−1〉}
C={〈1,1〉,〈1,2〉}.
Find the change of coordinates matrix...
Consider the following two ordered bases of R^2:
B={〈1,−1〉,〈2,−1〉}
C={〈1,1〉,〈1,2〉}.
Find the change of coordinates matrix from the basis B to the
basis C.
PC←B=?
Find the change of coordinates matrix from the basis C to the
basis B.
PB←C=?
Let M = ( (−3 1 3 4), (1 2 −1 −2), (−3 8 4 2))...
Let M = ( (−3 1 3 4), (1 2 −1 −2), (−3 8 4 2))
14. (3 points) Let B1 be the basis for M you found by row
reducing M and let B2 be the basis for M you found by row reducing
M Transpose . Find the change of coordinate matrix from B2 to
B1.