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Linear Algebra: simple matrix proof 1. If matrix A of order n satisfies a ^ 3 = 3A (A-I), it is proved that I-A is invertible and (I-A) ^ (- 1) is obtained 2. Let a, B and C be matrices of the same order, and C be nonsingular. Satisfy C ^ (- 1) AC = B. prove: C ^ (- 1) a ^ MC = B ^ M
1、
A^3=3A(A-I),
A^3-3A^2+3A -I=-I
(I-A)^3=I,
(I-A) is reversible, and (I-A) ^ (- 1) = (I-A) ^ 2
2、C^（-1）AC=B.
(C^（-1）AC)(C^（-1）AC).(C^（-1）AC)=B^m
=C^（-1）(A^m)C
3 × 3 matrix A = {4,2,3,1,1,0, - 1,2,3}, ab = a + 2B, find B
As the title, a = {4 2 3}
1 1 0
-1 2 3｝
AB = a + 2B, find B
AB=A+2B
AB-2B=A
AB-2EB=A
(A-2E)B=A
[(A-2E)^(-1)](A-2E)B=[(A-2E)^(-1)]A
EB=[(A-2E)^(-1)]A
B=[(A-2E)^(-1)]A
B=[(A-2E)*]A/│A-2E│
B=(3,-8,-6;2,-9,-6;-2,12,9)
Let a = {41 - 1; 211 2; 303}, and ab = a + 2B, find the matrix B
Because the foundation is not very good,
It's hard
There is a column of numbers 0 3 8 15 24 35. What is the number 50
They are the complete square minus one
So item 50 is the square of 50 minus 1 = 2499
-Square of 4 + 3 / 8 cube
(- 4 × - 4) + 3 / 8 × 3 / 8 × 3 / 8 = 16 + 27 / 512 = 16 and 27 / 512
Questions 1 and 3 on page 85 of physics in grade 2 of junior high school
I forgot my book
It took some time to find the irrational number in the second day of junior high school. Is it urgent? 1. Some people say that the weather of snowmelt is sometimes colder than snow. Is this statement reasonable? Personal point of view: reasonable. Melting absorbs heat. 3. This question has a picture, so I can only tell you the question and the answer. Question: according to the characteristics of the picture, we can judge that this material is a kind of
One pocket contains six small balls of the same shape and size, including two white balls, two red balls and two yellow balls
Ask: (1) the probability that two balls are yellow balls
(2) The probability of two balls having different colors
Please give me a list, reward points!
1.1/15
Touch the first ball, is from six out of a basketball, the probability is 2 / 6
To touch the second ball is to touch the remaining basketball out of five. The probability is 1 / 5
Multiplying the two is the probability of touching two basketballs
2.4/5
After touching the first ball, no matter what color it is, it is required that the two colors are different, that is, from the remaining five to touch the other four different from it, so the probability is 4 / 5
Since 100 square meters is equal to hectare, why should there be hectare?
Hectare is the metric unit of area. A piece of land with an area of one hectare is similar to a standard football field
The master does one third more work than the apprentice, and the apprentice spends one eighth more time than the master. What percentage of the apprentice who asks for the master's work efficiency
The ratio of master to apprentice is 4:3
The ratio of working hours of master and apprentice is 8:9
Then the ratio of master to apprentice is 4 / 8:3 / 9 = 3:2
Master's work efficiency is 150% of apprentice's
The difference between a and B is 9. One sixth of a is equal to one fourth of B. what is a? What is B?
The number a is 27 and the number B is 18
1： Let a be x and B be y
x-y=9,
x/6=y/4.
The solution is x = 27, y = 18
2： Let one sixth of the number a be x, then one fourth of the number B be X. so the number a is 6x and the number B is 4x
6x-4x=9.
2x=9
x=4.5
So the number a is 6x = 6 * 4.5 = 27, and the number B is 4x = 4 * 4.5 = 18
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