select four statements from the invertible matrix theorem and show that all four statements are true or false
this learning module introduced the invertible matrix theorem. this theorem is a collection of 12 equivalent statements. this means that when one statement in the theorem is true, all statements in the theorem are true. similarly, when one statement in the theorem is false, all statements are false. for your initial post, propose a specific n x n matrix a, where n > = 3. select four statements from the invertible matrix theorem and show that all four statements are true or false, depending on the matrix you selected. make sure to clearly explain and justify your work. also, make sure to label your statements using the notation used in the notes (e. g., part (a), part (f),
theorem (the invertible matrix theorem): let a be an n x n matrix. then the following statements are equivalent:
a is an invertible matrix.
a is row equivalent to the n x n identity matrix.
a has n pivot positions.
the equation ax = 0 has only the trivial solution.
the columns of a form a linearly independent set.
the linear transformation x à ax is one-to-one.
the equation ax = b has at least one solution for each b in pastedimage_ohc3rrwkynqmcj5zzf3co6f lld6y.
the columns of a span pastedimage_pzfbc6caq6376idt98x6kbg bja3r.
the linear transformation x à ax maps pastedimage_q19dyrqa66w6pzkvd6qntye ubll3 onto pastedimage_dmc0illlvzpimrjuv5soz2g 0p5cb.
there is an n x n matrix c such that ca = i.
there is an n x n matrix d such that ad = i.
at is an invertible matrix.

sorry not sure

step-by-step explanation:

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

aloha~! my name is zalgo and i am here to you out on this amazing day. to answer your question, yes, nonzero numbers can have a greatest common factor and that would be 1. still don't get it? let me considering every number is divisible by 1 and hence every number has 1 as a factor of theirs. so, if 2 nonzero numbers didn't share any gcf (greatest common factor), they would still have a factor in common and that would be 1.

i hope that this ! : p

"stay and stay proud! " - zalgo

(by the way, do you mind marking me as brainliest? i'd greatly appreciate it! mahalo! x3)

answer: the sun

explanation:

water cycle describes the evaporation of water from earth's surface, formation of clouds and precipitation water back onto the surface of earth. seventy percent of the earth is covered with water in the form of seas and oceans. the heat of the sun causes the evaporation of water from the surface of the ocean. the water vapors rise and condense to form water droplets. the collection of these water droplets form clouds which rain down again.

the evaporation of the oceans surface water as part of the water cycle is caused by the sun