If 3x + 1 = the absolute value of 2x-3, then the positive solution of X is ()

If 3x + 1 = the absolute value of 2x-3, then the positive solution of X is ()

3x+1=|2x-3|
2x-3=3x+1
X = - 4 (rounding off)
perhaps
2x-3=-3x-1
x=2/5
The positive solution of X is (2 / 5)
The determinant of matrix
Proof: for any two n-order homomorphic square matrices A and B
|AB|=|A|·|B|
It is to construct a matrix D of order 2n (represented by block matrix here)
D =
|A 0|
|C B|
This is an upper triangular matrix. It is easy to get | D | = | a | B|
(A and B are the original n-order matrices, O is the n-order matrix with all zeros, C is the n-order diagonal matrix with all the elements on the diagonal being - 1 and all the other elements being 0)
It is proved that | D | = | ab|
The elementary row transformation of matrix D (the specific process is very complicated, omitted) is transformed into the following form D=
|A M|
|C 0|
Where 0 is also an all zero matrix, the element M (I, J) = a (I, 1) B (1, J) + a (I, 2) B (2, J) +... + a (I, n) B (n, J), (it is easy to see that M is actually a matrix AB)
Take column n + 1, N + 2,..., 2n of D and expand the determinant by blocks,
D = （-1）^(1+2+3+..+n) * |C| * |M|
(C is a diagonal matrix whose diagonals are all - 1, and the value of its determinant is easy to obtain.)
There is | D | = | ab|
Given the square of X + the square of Y + the square of Z - 2x + 4y-6z + 14 = 0, find the square root of the algebraic formula x + y + Z
x^2+y^2+z^2-2x+4y-6z+14=0
(x^2-2x+1)+(y^2+4y+4)+(z^2-6z+9)=0
(x-1)^2+(y+2)^2+(z-3)^2=0
So x = 1, y = - 2, z = 3
So the square root of X + y + Z is root (1-2 + 3) = root 2
Finding the determinant of block matrix
ABCD is n-order square matrix, a is invertible, find | a, B, C, D |, find the specific process, and how to simplify the evaluation of block matrix determinants, and what operations can be carried out between determinants?
For the solution of this problem, see the figure below (click to enlarge it)
As for your other questions, I think it should be answered like this. Don't focus on the problem-solving methods first. Linear algebra is a system. Read the book several times to understand the system. When you are familiar with the theorems in the book and their proof methods, you will be close, because the methods of exercises can be found in the process of theorem proof
Given that (2x) & sup2; = 16, y is the square root of (- 5) & sup2;, find the value of the algebraic formula X / x + y + X / X-Y
|2x|=4,|x|=2
y=(-5)^2^(1/2)=5
x=2,y=5
x/(x+y)+x/(x-y)=2/7+2/(-3)=-8/21
x=-2,y=5
x/(x+y)+x/(x-y)=-2/3-2/(-7)=-8/21
Are you sure the algebraic expression X / x + y + X / X-Y is correct? It can be directly calculated as 2
From (2x) & sup2; = 16 we get 4x & sup2; = 16, X & sup2; = 4, x = 2 or x = - 2
Y is the arithmetic square root of (- 5) & sup2;, that is, y is the arithmetic square root of 25, so y = 5
When x = 2: X / x + y + X / X-Y =....
When x = - 2: X / x + y + X / X-Y =....
|2x|=4,|x|=2
y=(-5)^2^(1/2)=5
x=2,y=5
x/(x+y)+x/(x-y)=2/7+2/(-3)=-8/21
x=-2,y=5
x/(x+y)+x/(x-y)=-2/3-2/(-7)=-8/21
It is known that (2x) & sup2; = 16
4X²=16
X1=2
X2=-2
Y=5
x/x+y+x/x-y：
① The value of X is 2:1 + 5 + 1-5 = 2
② The value of X is - 2 1 + 5 + 1-5 = 2
③ The value of X is 2:2 △ 7 + 2 △ 3 = - 8 / 21
④ The value of X is - 2: - 2 / 3 + - 2 / 7 = - 20 / 21
Students can put the formula, or there are many algorithms..
(2x) & sup2; = 16 (- 5) & sup2; = radical y
2X = positive and negative root sign 4 root sign Y = 25
X = plus or minus 2, y = 5
So X1 = + 2, X2 = - 2
When x = 2, y = 5
Substituting X / (x + y) + X / (X-Y) yields - 8 / 21
When x = - 2, y = 5
Substituting X / (x + y) + X / (X... expansion
(2x) & sup2; = 16 (- 5) & sup2; = radical y
2X = positive and negative root sign 4 root sign Y = 25
X = plus or minus 2, y = 5
So X1 = + 2, X2 = - 2
When x = 2, y = 5
Substituting X / (x + y) + X / (X-Y) yields - 8 / 21
When x = - 2, y = 5
Substituting X / (x + y) + X / (X-Y) yields - 8 / 21
That ~ ~ ~ the final answer is the meter copied in front of me. The first one is right. Otherwise, the process is right and the answer is wrong. It's too sad ~ put it away
Matrix,
Let the third-order matrix A = [top to bottom a, 2C, 3D], and the third-order matrix B = [top to bottom B, C, D], where a, B, C, D are three-dimensional row vectors, and the determinant | a | = 18 and | B | = 2 are known, then the determinant | A-B | = 2
A.1,B.2,C.3,D.4
Give the idea
|A | = 6 | from top to bottom a, C, D | = 18, | from top to bottom a, C, D | = 3
|A-B | = | from top to bottom A-B, C, 2D | = 2 | from top to bottom A-B, C, D | = 2 [| from top to bottom a, C, D | - | B |] = 2
If 3x-5 and 1-x are the square roots of a number, what is x
1.5 or 2
3 / 2 question: are there any other answers
Is the determinant of the product of matrix A and B equal to the determinant of a multiplied by the determinant of B
Is the determinant of a + B equal to the determinant of a plus the determinant of B
Theorem 5.2 let AB be a square matrix of order n, then the determinant of the product matrix of a and B is equal to the product of the determinant of a and B
True, but AB is a matrix of order n
Is the determinant of a + B equal to the determinant of a plus the determinant of B
This is not true
5x & # 178; + 14xy + 7Y & # 178; = 0 to find the value of X + 2Y △ 5x + y is like this
X + 2Y and 5x + y are the formulas on the left side of the whole, which are 8y & # 178, not 7Y & # 178;
From 5x & # 178; + 14xy + 8y & # 178; = 0, (5x + 4Y) (x + 2Y) = 0
Then x = - 4Y / 5 or x = - 2Y, the original formula = - 2 / 5 or 0
1. Why is the sum of n eigenvalues of n-order matrix equal to the sum of elements on the main diagonal 2? Why is the multiplication of n eigenvalues equal to the determinant of the matrix
This is a theorem. There should be a proof in the textbook
The characteristic polynomial f (λ) = | a - λ e of a|
On the one hand, the coefficient and constant term of λ ^ n, λ ^ (n-1) are analyzed from the definition of determinant
On the other hand, f (λ) = (λ 1 - λ)... (λ n - λ)
By comparing the coefficients and constant terms of λ ^ n, λ ^ (n-1), the conclusion is obtained