Ask
your own question, for FREE!
Mathematics
46 Online
Let A be an nxn matrix and c a scalar. Show that det(cA) = c^n * det(A)
Still Need Help?
Join the QuestionCove community and study together with friends!
One property of the determinant is that if you multiply an entire row (or entire column) by some c then the new determinant is c*original. This is shown inductively: A = [a b] A' = [K*a K*b] det A = ad-bc [c d] [c d] det A' = Kad-Kbc = K*det A we then use the fact that the determinant of a 3x3 is found using 2x2 minors, or more generally (N+1)x(N+1) using NxN. This property is seen to remain true by induction. c*A where a is nxn is multiplying n rows by c, so if we remove a constant multiplication of a row one at a time we find c^n as a constant multiplied by the determinant, ie: det (cA) = c^n*det(A)
Can't find your answer?
Make a FREE account and ask your own questions, OR help others and earn volunteer hours!
Join our real-time social learning platform and learn together with your friends!
Join our real-time social learning platform and learn together with your friends!
Latest Questions
Yosad930:
okay another random question that even google itself isnt helping me with: why cant i zoom in and out anymore with the touchpad? yk how when you pinch your
AddieroniAndCheese:
Tips for studying for an AP exam in like a week? I barely know anything about chem T-T.
thereneelg:
Ok so. I need help. So for one of my songs in choir, The Power of Love. We have to hold one of the "Love"s for a long time.
Aniii:
What is the mean of the following set of numbers: 4, 8, 6, 5, 3? 5.0 5.2 6.0 7.0
gelphielvr:
(algebra 1) input data, revenue f(x) = initial amount(interest)^x question in the
Yosad930:
;-; exam is next tuesday, and i dont get a single thing (well maybe one or two) c
H1m:
What does tariffs mean and what are they exactly? I need an answer from someone that actually knows.
48 minutes ago
5 Replies
0 Medals
2 hours ago
3 Replies
1 Medal
50 minutes ago
12 Replies
1 Medal
11 hours ago
5 Replies
0 Medals
1 hour ago
10 Replies
1 Medal
2 hours ago
15 Replies
0 Medals
10 hours ago
13 Replies
3 Medals