1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nana76 [90]
4 years ago
5

Suppose CAequalsISubscript n ​(the ntimesn identity​ matrix). Show that the equation ABold xequalsBold 0 has only the trivial so

lution. Explain why A cannot have more columns than rows
Mathematics
1 answer:
ruslelena [56]4 years ago
7 0

Answer:

See Explanation

Step-by-step explanation:

(a)For matrices A and C, given that: CA=I_n.

We want to show that Ax=0 has only the trivial solution

If Ax=0

Multiply both sides by C

C(Ax)=C \times 0\\\implies (CA)x=0$ (Recall: CA=I_n)\\\implies I_nx=0 $ (Since I_n$ is the n\times n$ identity matrix)\\\implies x=0

This means that the system has only the trivial solution.

(b)If the system has more columns than rows, a free variable would occur when a column does not have a pivot. This would lead to a non-trivial solution.

You might be interested in
4 math questions plz help
Sonja [21]
The first one is the square root of 9 and 16

8 0
4 years ago
Unit 3: Parallel & Perpendicular Lines Homework 5: Linear Equations Slope-Intercept & Standard Form
Alona [7]
And you can see that I don’t have respect you don’t deserve that you
4 0
3 years ago
What does it mean in this situation if the average rate of change is​ negative?
WARRIOR [948]
It means that it is a rate that is decreasing or declining.
5 0
4 years ago
Read 2 more answers
of the oranges 48 in a carton, one-third of them were rotten. ben and david took the remaining good oranges. if ben took 8 more
GaryK [48]
Number of Good Oranges = 2/3 * 48 = 32

Now, Let the number of Oranges taken by David = x
Taken by Ben = x + 8

It is given that, x + x+8 = 32
2x = 32 - 8
x = 24/2
x = 12

In short, David takes 12 Oranges

Hope this helps!
4 0
4 years ago
Can Someone help with problems 2,3,4. Please
Ghella [55]
Number 2 is 990 because the numbers are 9, 10, and 11.
5 0
3 years ago
Other questions:
  • A baskets contains 34 heads of lettuce, 5 of which are spoiled. If a sample of 2 is drawn and not replaced, what is the probabil
    12·1 answer
  • A simple random sample of 36 men from a normally distributed population results in a standard deviation of 10.1 beats per minute
    11·1 answer
  • Karen wants to buy jeans at a store that is giving $10 off everything. The tag on the jeans is marked 50% off. The original pric
    13·2 answers
  • Which ordered pair is in the solution of the system of inequalities shown in the accompanying graph
    5·1 answer
  • Which of the following determines a plane?
    13·1 answer
  • HEY CAN ANYONE PLS ANSWER DIS MATH PROBLEM!
    9·1 answer
  • Please help and show work
    9·1 answer
  • Write an equation to the model above<br> BEST ANSWER GET BRANLIEST
    12·1 answer
  • PLEASE HELP I WILL GIVE BRAINLIEST!!!!
    9·1 answer
  • Write the slope-intercept form of the equation of each line given the slope and y-intercept.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!