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Nana76 [90]
3 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]3 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
Order the numbers from least to greatest 3 7/9 , 3.65 , 3.6
kvasek [131]

Answer:

3.6, 3.65, 3 7/9

Step-by-step explanation:

you just have to make all of the numbers decimals or mixed fractions then it is very easy to order them.

7 0
3 years ago
1. Average Senior High School annual cost of tuition fee for all private schools in Cavite last year was 46,300 a random sample
anygoal [31]

Answer:

Step-by-step explanation:

H0 : μ = 46300

H1 : μ > 46300

α = 0.05

df = n - 1 = 45 - 1 = 44

Critical value for a one tailed t-test(since population standard deviation is not given).

Tcritical = 1.30

The test statistic :(xbar - μ) ÷ (s/sqrt(n))

The test statistic, t= (47800-46300) ÷ (5600√45)

t = 1500

t = 1500 / 834.79871

t = 1.797

The decision region :

Reject H0: if t value > critical value

1. 797 > 1.30

Tvalue > critical value ; We reject H0

Hence, there is sufficient evidence to conclude that cost has increased.

5 0
2 years ago
What are the solutions of the equation x^4-9x^2+8=0? Use u substitution to solve.
vodka [1.7K]

Answer:

The answer is the second option

Step-by-step explanation:

Let u=x^2.

( {x}^{2} ) {}^{2}  - 9( {x}^{2} ) + 8( {x}^{2} ) {}^{0}

{u}^{2}  - 9u + 8

(u - 1)(u - 8)

u = 1

u = 8

Set this equal to x^2

{x}^{2}  = 1

x = 1

or

x =  - 1

{x}^{2}  = 8

x = 2 \sqrt{2}

or

x =  - 2 \sqrt{2}

4 0
1 year ago
kendra biked 10kilometers on monday .she biked twice as many kilometers on tuseday how many total meters did she bike
hram777 [196]

Answer:

10km+10km*2 = 30km

30km*(1000m/1km) = 30000m

In the second equation of the problem, the kilometers from the initial total distance biked is cancelled out by the conversion of kilometers to meters, as seen in the 1000m/1km (or 1000 meters for every 1 kilometer).

Read more on Brainly.com - brainly.com/question/454009#readmore

Step-by-step explanation:

5 0
3 years ago
An isosceles triangle has a perimeter (9y-15)cm. what is the length of the remaining equal sides of it's third side is (3y-7) cm
ozzi

The length of each of the equal sides is become x = (3y-4) cm

According to the statement

we have given that the perimeter of the isosceles triangle and length of third side. and we have to find the length of same side of triangle.

So,

An isosceles triangle is a triangle that has two sides of equal length.

Let the equal sides of isosceles triangle be x cm each.

We know that the

Sum of sides of a triangle = perimeter

x+x+(3y-7) = 9y-15

2x = 9y-3y-15+7

After solving the equation it become

2x= 6y-8

x=(6y-8)/2

Now the length of equal sides is x=3y-4

So, The length of each of the equal sides is become x = (3y-4) cm

Learn more about isosceles triangle here

brainly.com/question/1475130

#SPJ1

7 0
2 years ago
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