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
const2013 [10]
2 years ago
9

Suppose ADequalsISubscript m ​(the mtimesm identity​ matrix). Show that for any Bold b in set of real numbers R Superscript m​,

the equation ABold xequalsBold b has a solution.​ [Hint: Think about the equation ADBold bequalsBold b​.] Explain why A cannot have more rows than columns.
Mathematics
1 answer:
horrorfan [7]2 years ago
5 0

Answer:

See Explanation

Step-by-step explanation:

(a)For matrices A and D, given that: AD=I_m.

We want to show that \forall b \in R^m, Ax=b has a solution.

If Ax=b

Multiply both sides by D

(Ax)D=b \times D\\\implies (AD)x=bD$ (Recall: AD=I_m)\\\implies I_mx=Db $ (Since I_m$ is the m\times m$ identity matrix)\\\implies x=Db

This means that the system Ax=b has a solution.

(b)Matrix A has a pivot position in each row where each pivot is a different column. Therefore, A must have at least as many columns as rows.

This means A cannot have more rows than columns.

You might be interested in
BRAINLIEST AND POINTS!!!<br><br> PLEASE EXPLAIN
timofeeve [1]

Answer:

Option C. \$23,134.61

Step-by-step explanation:

we know that

A=\frac{P[(1+r)^{n} -1]}{r(1+r)^{n}}

we have

P=\$400

r=0.075/12=0.00625

n=6*12=72\ months

substitute in the formula

A=\frac{400[(1+0.00625)^{72} -1]}{0.00625(1+0.00625)^{72}}\\ \\A=\frac{226.446972}{0.009788}\\ \\A=\$23,134.61

4 0
2 years ago
Three more than twice a number is equal to four less than number .Find the number​
Marina86 [1]
The number is -7, hope this helps!
6 0
2 years ago
Kelly is in a hot air balloon that has just taken off and is now floating 7 meters above its launching point. Denise is standing
irina1246 [14]

Answer:

9.9 meters

Step-by-step explanation:

Given that the distance between Kelly and launching point was 7m and also the distance between launching point and Dennis was also 7m, to calculate for the distance between Kelly and denise is done by applying the formula used for calculating the hypotenuse in a right angle triangle (the shape that was created)

PICTURE ATTACHED IS A DETAILED STEP BY STEP PROCESS OF HOW 9.9m WAS GOTTEN.

8 0
3 years ago
This is for my Maths homework but I really don't know how to do the second one. Could someone please help.
Taya2010 [7]
Those tiny bars crossing those segments mean they are congruent
therefore you have isosceles triangles there
angles opposing congruent sides in isosceles triangles are also congruent
so
the other 2 angles in the 24 degrees triangle are (180-24)/2=78 degrees
now the angle close to the 24 from the 44 degrees triangle is also 78, that means that the third angle in the 44 triangle is 180-44-78=58
also the angle close to y is 58 (because of isosceles)
therefore y = 180-58=122 degrees
7 0
3 years ago
Read 2 more answers
june made a design with 6 equql tiles.One tile is yellow,2 tile iare blue and 3 tiles are purple. what fraction of the tiles are
Rudiy27
It would be 2/3 because u add the one yellow and three purple to make 4 (put that on the numerator) and the 6 would go on the denominator to make 4/6 then u divide each by two to reduce to get 2/3
4 0
3 years ago
Other questions:
  • Fanning + medal
    7·2 answers
  • How much less is -200m than 450m?
    5·1 answer
  • Joey Chestnut is trying to break his own world record for eating the most hotdogs and buns in 10 minutes he needs to eat more th
    12·1 answer
  • How do I solve this ?
    6·1 answer
  • What is the domain of f(x) = -(x-6)^2-30
    6·1 answer
  • If you flip a pair of coins 48 times, how many times are you most likely to get 2 heads.
    11·1 answer
  • ASAP<br> Can someone please helppp
    12·1 answer
  • What is f(4) for the function f(x)= 6x+7?
    14·1 answer
  • Locate the b term in the equation.
    15·1 answer
  • Alice rode her bicycle the same number of miles every day for 17 days. She
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!