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
Minchanka [31]
3 years ago
10

Show that if A and B are similar nxn matrices, then det(A)=det(B).

Mathematics
1 answer:
natita [175]3 years ago
7 0

Step-by-step explanation:

To prove it we just use the definition of similar matrices and properties of determinants:

If A,B are similar matrices, then there is an invertible matrix C, such that A=C^{-1}BC} (that's the definition of matrices being similar). And so we compute the determinant of such matrix to get:

det(A)=det(C^{-1}BC)=det(C^{-1})det(B)det(C)

=\frac{1}{det(C)}det(B)det(C)=det(B)

(Determinant of a product of matrices is the product of their determinants, and the determinant of C^{-1} is just \frac{1}{det(C)})

You might be interested in
How to solve which one is closest to 27.8 × 9.6
NARA [144]
27.8 × 9.6=266.88 and if rounded its 267.0(:
6 0
3 years ago
) One year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million. Suppose a samp
Nutka1998 [239]

Answer:

Probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

Step-by-step explanation:

We are given that one year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million.

Suppose a sample of 400 major league players was taken.

<em>Let </em>\bar X<em> = sample average salary</em>

The z-score probability distribution for sample mean is given by;

                 Z = \frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }  ~ N(0,1)

where, \mu = mean salary = $1.5 million

            \sigma = standard deviation = $0.9 million

             n = sample of players = 400

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the average salary of the 400 players exceeded $1.1 million is given by = P(\bar X > $1.1 million)

    P(\bar X > $1.1 million) = P( \frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} } >  \frac{ 1.1-1.5}{{\frac{0.9}{\sqrt{400} } }} } ) = P(Z > -8.89) = P(Z < 8.89)

<em>Now, in the z table the maximum value of which probability area is given is for critical value of x = 4.40 as 0.99999. So, we can assume that the above probability also has an area of 0.99999 or nearly close to 1.</em>

Therefore, probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

4 0
3 years ago
How can you use number patterns to find the least common multiple of 120 and 360
baherus [9]
<span>Since 360 is a multiple of 120, it is automatically the LCM of this problem.

</span>
8 0
3 years ago
PLEASE PLEASE HELP PLEASE
kogti [31]

Answer:

r = 6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

PR² = PQ² + QR² , substitute values

(r + 4)² = r² + 8²

r² + 8r + 16 = r² + 64 ( subtract r² from both sides )

8r + 16 = 64 ( subtract 16 from both sides )

8r = 48 ( divide both sides by 8 )

r = 6

3 0
2 years ago
Simplify this expression
antiseptic1488 [7]

Answer:

2/(3x-2)²

Step-by-step explanation:

4x²-6x³-2x²+6x³/4x²-6x³-6x³+9x^4=

2x²/4x²-12x³+9x^4=

2x²/x²(4-12x+9x²)=

2/9x²-12x+4

2/(3x-2)²

6 0
3 years ago
Other questions:
  • 2x to the second power subtract 9x
    7·2 answers
  • Please help ASAP!!!
    8·1 answer
  • How many squares would have to be shaded so that<br> of the shape is shaded?
    11·1 answer
  • What’s the definition of prime
    9·1 answer
  • 3x√64= please help meee
    7·2 answers
  • Fifteen percent of the students in seventh grade at Western Middle School have perfect attendance. There are 220
    15·1 answer
  • F(x)=15x³+22x²-15x+2<br> Write f(x) as a product of linear factors.
    11·1 answer
  • Does anyone know this?<br> 16 − 7v &lt; 2
    8·2 answers
  • Parallel lines j and k are cut by transvesal t . Which statement is true about ∠2 and ∠6
    7·2 answers
  • Mrs.Li has 107 beehives . She harvested about 64 kg of honey per hive. About how many kilograms of honey did Mr.s Li Harvest
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!