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
Dafna11 [192]
2 years ago
14

Select four statements from the invertible matrix theorem and show that all four statements are true or false

Mathematics
1 answer:
Lelechka [254]2 years ago
5 0

Answer:

A) A is an invertible matrix ( TRUE )

B) A is a row equivalent to the n x n identity matrix ( n = 3 ) ( TRUE )

C ) The equation Ax = 0 has only the trivial solution ( TRUE )

D ) The columns of A form a linearly independent set ( TRUE )

Step-by-step explanation:

Assuming a matrix A

\left[\begin{array}{ccc}1&2&1\\-1&0&3\\4&1&5\end{array}\right]

det A = 1 [ 0 -3 ] +  2 [12 + 5 ]  + 1[-1]

        = -3 + 34 -1 = 30 ≠ 0

THEREFORE  det A = 30 ≠ 0

Attached is the detailed solution of the given statements above

You might be interested in
BEST ANSWER GETS BRAINLIEST!!!!PLEASE HELLPP
Sonja [21]
1/3b = 4/5
Do the cross multiplication
1(5) = 3b(4)
5=12b
<span>b=5/12</span>
4 0
3 years ago
Find the center and radius of the circle with equation (x + 8)2 + (y + 3)2 = 49.
SashulF [63]
Center is at (h,k) in standard form:
(x-h)2 + (y-k)2 = r2
Center: (-8, -3)
Radius (r): sr49 = 7
3 0
3 years ago
Read 2 more answers
A population of 360 field mice live inside of a small area of forest near your house.240 of the mice are brown, and 120 of the m
OlgaM077 [116]
It would be about 33%
4 0
3 years ago
What does 144 =to for a squared
Dafna11 [192]
12 *12 = 144

Therefore 12^2 = 144
5 0
2 years ago
Read 2 more answers
In the past, 21% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research firm ha
Afina-wow [57]

Answer:

A sample size of 79 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

\pi = 0.21

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.  

What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09?

A sample size of n is needed.

n is found when M = 0.09. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.09 = 1.96\sqrt{\frac{0.21*0.79}{n}}

0.09\sqrt{n} = 1.96\sqrt{0.21*0.79}

\sqrt{n} = \frac{1.96\sqrt{0.21*0.79}}{0.09}

(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.21*0.79}}{0.09})^{2}

n = 78.68

Rounding up to the nearest whole number.

A sample size of 79 is needed.

4 0
3 years ago
Other questions:
  • An exercise teacher wants each student in her class to have at least 48 square feet of space on the floor. What is the largest n
    14·1 answer
  • PLEASE HELP ME!!!!!!!Which expression is equivalent to 6x2−(4x+10)−3+(4x2−5x)?
    6·1 answer
  • What is m&lt;6 please help
    8·1 answer
  • Write i. word form 209.106​
    10·2 answers
  • How do you solve 2(3x+7)-5(x+3)?
    7·2 answers
  • A researcher conducts two studies on the effectiveness of a peer mentoring program. Self-evaluation ratings among participants b
    13·1 answer
  • What two numbers have a product of -36 and a sum of<br> 5?
    6·1 answer
  • Solve for x in terms of c 3(cx-7)=9
    5·1 answer
  • What is the equation of a line that has the same slope as y=7-2x and the same y-intercept as y=-7x-5
    13·1 answer
  • Megan is one of the cheerleaders in her school. To prepare for the forthcoming Cheer Dance Competition, her coach is teaching th
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!