Let a matrix of order 3 be a = | 1,2,3 2,1,3 3,3,6 |, Find the invertible matrix P such that P ＾ - 1) AP = a

Let a matrix of order 3 be a = | 1,2,3 2,1,3 3,3,6 |, Find the invertible matrix P such that P ＾ - 1) AP = a

Solution: | a - λ e | = λ (9 - λ) (1 + λ). So the fundamental solution system of a with eigenvalues of 0,9, - 1ax = 0 is: A1 = (1,1, - 1) '(a-9e) x = 0 is: A2 = (1,1,2)' (a + e) x = 0 is: A3 = (1, - 1,0) 'let the matrix P = (A1, A2, A3), then p ^ (- 1)

Find the inverse of this matrix. The first behavior is 1,2,3, the second behavior is 0,1,2, and the third behavior is 0,0,1

Inverse matrix: the first behavior is 1, - 2,1, the second behavior is 0,1, - 2, and the third behavior is 0,0,1

The inverse matrix of diagonal matrix

AIJ is the algebraic cofactor of the element AIJ in matrix A (AIJ). Matrix A * (AIJ) becomes the adjoint matrix of a, d = | a |, and the matrix of a = 1 / D × a*
This is what the book says, but adjoint matrix is very difficult to find, usually do the problem is not so inverse matrix
Instead, we make an n × 2n matrix (a, e) and transform its left half into e by elementary row transformation. At this time, the right half is the inverse matrix of A

What is the actual length and width of the 9-inch screen 16:9?

A wide screen: length and width pixels: 1366:768 inches: 9 converted into cm * 2.54 = 22.86 cm. According to Pythagorean theorem, the length of bevel edge pixels is 1567.09285 pixels. The pixels within 1cm are: (total pixels / total cm) 68.55174321 pixels, so the width is 〓 19.92655381 cm, and the height is 〓 11.2032162 cm B

Xiao Hua read a book. On the first day, he read 18 pages more than 21, and on the second day, he read 16 pages less than 6, with 172 pages left. How many pages are there in this story book?

Suppose there are x pages in this story book, the number of pages read on the first day: 18x + 21, the number of pages read on the second day: 16x-6, X - (18x + 21) - (16x-6) = 172, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X -- 18x-21-16x + 6 = 172, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X -- 18x-16x + 6-21 = 172, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp;   1724X-15=172，            1724X-15+15=172+15，                  1724X=187，             1724X÷1724=187÷1724，    &A: there are 264 pages in this storybook

In mathematics class, teacher Zhang of class one, grade seven, wrote a question to the students: "when a = 2, B = - 2, find a polynomial
To find the value of the polynomial 3A & # 179; B & # 179; - AB + B - (4a & # 179; B & # 179; - ab-b) + (A & # 179; B & # 179; + AB) - 2b + 3 ", Ma Xiaohu copied a = 2 wrongly into a = - 2, Wang Xiaozhen did not copy the wrong question, but they all made the same results. Do you know what happened?

The original formula = 3A & # 179; B & # 179; - AB + b-4a & # 179; B & # 179; + AB + B + A & # 179; B & # 179; + ab-2b + 3 (without brackets)
=3A & # 179; B & # 179; - 4A & # 179; B & # 179; + A & # 179; B & # 179; - AB + AB + B + b-2b + 3 (transfer)
=ab+3
The result of polynomial reduction is ab + 3
The result is not affected by the sign of ab
The results are all the same

The distance between bus and car is 360 kilometers. Bus runs 60 kilometers per hour, and car runs later than bus
1.5 hours. As a result, the two cars arrive at a certain place at the same time, and the speed of the car is calculated

It is assumed that the speed of the car is x km / h
360÷60-360÷x=1.5
6-360/x=1.5
360/x=4.5
x=80
It is tested that x = 80 is the root of the equation

If the two sides of an isosceles triangle are 5cm and 8cm respectively, how many cm is the maximum perimeter and how many cm is the minimum perimeter of an isosceles triangle

There are two cases
1. If the waist length is 5cm, the other waist length is 5cm and the bottom edge length is 8cm, so the circumference is 5 + 5 + 8 = 18cm
2. If the waist length is 8cm, the other waist length is 8cm, and the bottom length is 5cm, so the circumference is 8 + 8 + 5 = 21cm
At least 18cm, at most 21cm

It takes 10 hours for a bus to go from city a to city B, and 15 hours for a truck to go from city B to city A. the two cars leave each other. When they meet, the bus is 192 kilometers away from city B. how many kilometers is the distance between the two cities?

If the speed ratio of a and B is 110:115 = 3:2, the whole journey is 192 △ 23 + 2 = 192 △ 25, = 480 km. A: the distance between the two places is 480 km

Definition: A is a rational number that is not 1, and the 1-A is called the difference reciprocal of A. for example, the difference reciprocal of 2 is 1-2 = - 1;
-If A1 = - 1 / 3, A2 is the difference reciprocal of A1, A3 is the difference reciprocal of A2, A4 is the difference reciprocal of A3 And so on, find the value of a2013

a2013=4
Please click the [praise] button in the lower right corner in time
∵ a1=-1/3
∴a2=1/[1-(-1/3)]=1/(4/3)=¾
a3=1/(1-¾)=1/(¼)=4
a4=1/(1-4)=-1/3
……
It can be seen from the above calculation that the result is a set of values that will appear in a cycle, A4 = A1, A5 = A2, A6 = A3
Period = 3
2013÷3＝671.0
The remainder is 0
∴a2013=a3=4