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Posted: **Thu Jun 30, 2022 7:35 pm**

: The Rank Of The Matrix A Is Its Most Important Property There Are Many Equivalent Ways Of Characterizing The Rank Rank 1 (33.71 KiB) Viewed 42 times

ways of characterizing the rank:
rank(A) is the number of pivots in an echelon form of A
rank(A) is the dimension of the column space and row space of A
rank(A) is the size of the largest set of independent columns of A
PART A) Let y be a vector in I3 and A is a 3 × 3 matrix with columns » 24 3u What
are the possible values for rank(A)? Justify your answer.
PART B) Let 0, w be vectors in IR?. Let A be a matrix with 4 columns
0, w, 20 + w, v - w. What are the possible values for rank(A)? Justify your answer.
(Hint: for this question you

: The Rank Of The Matrix A Is Its Most Important Property There Are Many Equivalent Ways Of Characterizing The Rank Rank 2 (33.71 KiB) Viewed 42 times

The rank of the matrix A is its most important property. There are many equivalent ways of characterizing the rank: rank(A) is the number of pivots in an echelon form of A rank(A) is the dimension of the column space and row space of A rank(A) is the size of the largest set of independent columns of A PART A) Let u be a vector in R³ and A is a 3 x 3 matrix with columns v, 2v, 3v. What are the possible values for rank(A)? Justify your answer. PART B) Let u, w be vectors in R³. Let A be a matrix with 4 columns v, w, 2v+w, vw. What are the possible values for rank(A)? Justify your answer. (Hint: for this question you may want to consider the third characterization of rank listed above)