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
kirill115 [55]
2 years ago
6

The notation Ak meas the matrix A Multiplied with itself k times (a) For the 2×2 identity matrix I, show that I2 =I (b)For the n

×n identity matrix I, show that I2 =I (c) what do you think the enteries of Ik are?

Mathematics
1 answer:
djverab [1.8K]2 years ago
6 0

Answer:

Entries of I^k are are also identity elements.

Step-by-step explanation:

a) For the 2×2 identity matrix I, show that I² =I

I^{2}=\left[\begin{array}{cc}1&0\\0&1\end{array}\right] \times \left[\begin{array}{cc}1&0\\0&1\end{array}\right] \\\\=\left[\begin{array}{cc}1\times 1+0\times 0&1\times 0+0\times 1\\0\times 1+1\times 0&0\times 0+1\times1\end{array}\right] \\\\=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]

Hence proved  I² =I

b) For the n×n identity matrix I, show that I² =I

n×n identity matrix is as shown in figure

Elements of identity matrix are

\delta I_{ij}=1\quad if\quad i=j\\\delta I_{ij}=0\quad if\quad i\ne j\\

As square of 1 is equal to 1 so for n×n identity matrix I, I² =I

(c) what do you think the enteries of Ik are?

As mentioned above

\delta I_{ij}=1\quad if\quad i=j\\\delta I_{ij}=0\quad if\quad i\ne j\\

Any power of 1 is equal to 1 so kth power of 1 is also 1. According to this Ik=I

You might be interested in
Ill mark brainlist plss help
Hatshy [7]

Answer:

\frac{3×7}{5×7}   \frac{21}{35}

5 0
2 years ago
Round 6.443 to the nearest hundredth.
Gnesinka [82]
6.44 hope this helps
6 0
3 years ago
Read 2 more answers
A welder drops a piece of red-hot steel on the floor. The initial temperature of the steel is 2,500 degrees Fahrenheit. The ambi
sergey [27]

Answer: After 18.05 minutes, the temperature of steel becomes 100 degrees.

Step-by-step explanation:

Since we have given that

Initial temperature = 2500

At t = 0,

we get that

f(t)=Ce^{-kt}+80\\\\2500=C+80\\\\2500-80=C\\\\2420=C

After 2 minutes, the temperature of the steel is 1500 degrees.

so, it becomes,

1500=2420e^{-2k}+80\\\\1500-80=2420e^{-2k}\\\\\dfrac{1420}{2420}=e^{-2k}\\\\0.587=e^{-2k}\\\\\ln 0.587=-2k\\\\-0.533=-2k\\\\k=\dfrac{0.533}{2}\\\\k=0.266

So, We need to find the number of minutes when the temperature of steel would be 100 degrees.

So, it becomes,

100=2420e^{-0.266t}+80\\\\100-80=2420e^{-0.266t}\\\\20=2420e^{-0.266t}\\\\\dfrac{20}{2420}=e^{-0.266t}\\\\\ln \dfrac{20}{2420}=-0.266t\\\\-4.8=-0.266t\\\\t=\dfrac{4.8}{0.266}\\\\t=18.05

Hence, after 18.05 minutes, the temperature of steel becomes 100 degrees.

7 0
3 years ago
A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?
kolezko [41]
(x-center)^2+(y-center)^2=r^2
x^2+y^2=r^2
(5)^2+(-12)^2=r^2
25+144=r^2
169=r^2
r=13
5 0
3 years ago
Read 2 more answers
What differentiates extension from hyperextension?
SpyIntel [72]
I think its B

Correct me if this is wrong
4 0
3 years ago
Read 2 more answers
Other questions:
  • Convert the repeating decimal into a fraction: 0.555
    9·1 answer
  • explain how you can use a box-and-whisker plot to find the range of a data set. a. the range is the difference of the values of
    5·1 answer
  • The formula for the volume of a sphere is V=4/3 3.14r^3. What is the formula solved for r?
    10·1 answer
  • Check all the statements that are true:
    14·1 answer
  • adult tickets for the fall play cost $6 and students cost $3. the drama club so 25% more students tickets than adult tickets to
    12·1 answer
  • Is the following correspondence a function? <br>Yes or No?
    15·1 answer
  • Three consecutive integers have a sum of 51 find the integers
    9·2 answers
  • What number must be added to x^2+6x+7 to form a perfect square
    7·1 answer
  • What are the vertices of AA'B'C'if AABC is dilated by a scale factor of 4?
    11·1 answer
  • A woman has a total of $9,000 to invest. She invests part of the money in an account that pays 7 % per year and
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!