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Vector midpoint proof In the known isosceles triangle ABC,∠C=90°, D is the midpoint of CB, E is the point on AB, and AE=2EB.
Let CA=a, CB=b (the above arrows are omitted), then we can calculate BA=a-b, AD=1/2b-a, CE=b+1/3(a-b)=1/3a+2/3b; calculate AD·CE=(1/2b-a)·(1/3a+2/3b)=1/3b-1/3a-1/2ab; angle C is right angle, ab=0, CA=CB, b=a, so AD·C...
ON VECTORS IN COLLEGE MATHEMATICAL PROOF Let A and B be square matrices of order n and the determinant of A be equal to 2. 2 Proves that if n-dimensional unit vectors e1, e2... en can be linearly represented by a set of dimensional vectors a1, a2... an, then the set of vectors a1, a2... an is linearly independent
1.|A|=0, so A is reversible, and its inverse matrix is denoted as P.
Thus BA=EBA=(PA) BA=P (AB) A
AB is similar to BA by definition of similarity
2. If the n-dimensional unit vectors e1, e2... en can be linearly represented by the set of dimensional vectors a1, a2... an, then the two sets of vectors are known to be equivalent so as to have the same rank.
I don't know. Is that okay?
Prove:|b vector-a vector |a vector |-|b vector | Prove:|b vector-a vector a vector |-|b vector | Prove:|b vector-a vector | a vector |-|b vector |
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For any two vectors a, b, there is ||a|-|b a-b a b|
Let θ=first left:||a|-|b a-b|from |a-b|2-||a|-|b||2=(a2-2|a||b|cos b2)-(a2-2|a||b b2)=2|a||b|b|(1-cosθ)≥0, then right:|a-b a|-|b||:
Proving that (λa) b=λ(ab)=a (λb) Such as ~ Proving that (λa) b=λ(ab)=a (λb) For example ~
If the angle between a and b is x, then λa and b, a and λb are also x
The values are λabcosx (where a, b are the moduli of vectors a, b)
If the angle between a and b is x, then λa and b, a and λb are also x
Then all values are λabcosx (where a, b are the moduli of vectors a, b)
As shown in the figure, in the isosceles trapezoidal ABCD, E is the midpoint of CD, EF⊥AB is F, and if AB=6, EF=5, the area of the trapezoidal ABCD is ______. As shown in the figure, in the isosceles trapezoid ABCD, E is the midpoint of CD, EF⊥AB is F, and if AB=6, EF=5, the area of the trapezoid ABCD is ______.
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RELATED INFORMATIONS
- 1. Let the sum of the elements of any row of matrix A of order n be a and prove that a is a eigenvalue of matrix A to find the eigenvector corresponding to a Let a be the sum of the elements of any matrix A of order n be a and prove that a is a eigenvalue of matrix A to find the eigenvector corresponding to a
- 2. What does n-dimensional vector mean
- 3. What is the difference between n-dimensional unit column vector and n-dimensional unit vector
- 4. A is n-dimensional orthogonal matrix, a, b is n-dimensional column vector, then Aa·Ab=a·b. Why?
- 5. Given vector a=(x^2-3,1) b=(x,-y), when x <2 in absolute value, there is a⊥b, when x≥2 in absolute value, a‖b Given vector a=(x^2-3,1) b=(x,-y),(where y and x are not equal to 0), when x <2 in absolute value, there is a⊥b, when x≥2 in absolute value, a‖b, find function y=f (x)
- 6. The vector a=(cosα, sinα), b=(cosβ, sinβ),0<β<α If |a-b|=root2 find a perpendicular b let c=(0,1) if a+b=c find the value of The vector a=(cosα, sinα), b=(cosβ, sinβ),0<β<α If |a-b|=rootoot 2, find a perpendicular b Let c=(0,1) If a+b=c, find the value of
- 7. What is the difference between quantity product and vector product? Why the quantity product is perpendicular if the vector a* vector b=0 and the vector a* vector b=0 if the vector product is parallel What is the area of the quantity product and the vector product? Why is the quantity product vertical if the vector a* vector b=0 and the vector product parallel if the vector a* vector b=0?
- 8. Vector a+b=(-2,-1), a-b=(4,-3), the angle between vector a, b is
- 9. Given that M={ a|a=(2 1,-2-2), R}, N={ b|b=(3 2,6 1), R}, is a set of vectors, then M∩N= Options have four A {c|c (-2,1)} B {c|c (2,1)} C {c|c (-2,1)} D {c|c (2,1)}
- 10. Given that point D is the midpoint of the edge BC of the triangle, there is a point P in the plane where the triangle ABC is located, which satisfies vector PA + vector BP + vector CP =0, The module of vector PA is divided by the module of vector PD is equal to λ, and the value of λ is obtained.
- 11. Is a linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, then they are called orthogonal vector sets "orthogonal to any two vectors? Linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, it is called orthogonal vector set "is any two vectors orthogonal? Linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, then it is called orthogonal vector set "Is any two vectors orthogonal?
- 12. For the vector a, b, c and the real number λ, is the true proposition () in the following propositions possible to analyze these four in detail? A. If a*b=0, then a=0 or b=0 B. If λa=0, then λ=0 or a=0 C. If a^2= b^2, then a = b or a =-b D. If a*b=a*c, then b=c For the vector a, b, c, and real number λ, could the following real proposition () analyze these four in detail? A. If A*B=0, then A=0 or B=0 B. If λa=0, then λ=0 or a=0 C. If A2= B2, then A = B or A = B D. If a*b=a*c, then b=c
- 13. N +1 n-dimensional vector, composed of vector group dimension linear (? ) Vector Group N +1 n-dimensional vector, the vector group composed of linear (? ) Vector Group
- 14. It is proved that in n-dimensional vector space, if α1.α2...αn is linearly independent, then any vector β can be linearly represented by α1.α2..αn. It is proved that any vector β can be linearly represented by α1.α2...α n if α1.α2...
- 15. Let A be the s×m matrix, B be the m×n matrix, and X be the vector of n-dimensional unknown columns. Let A be the s×m matrix, B be the m×n matrix, and X be the vector of n-dimensional unknown columns. AB has the same rank as B, i.e. r (AB)=r (B) Let A be the s×m matrix, B be the m×n matrix, and X be the vector of n-dimensional unknown columns. Let A be the s×m matrix, B be the m×n matrix, and X be the vector of n-dimensional unknown columns. AB has the same rank as B, i.e. r (AB)= r (B)
- 16. Let A be a real matrix of m*n and A^TA be a positive definite matrix. It is proved by data that r (A^TA)≤r (n)≤n, but I don't know where this formula comes from, and the formula is r (AB)≤r (A), r (AB)≤r (B),. I've found the problem in the book, and now there's another question: Shouldn't r (A)≤min {m, n}? Why is the formula directly r (n)≤n? Somebody help me.
- 17. Matrix proof: If the matrix of order n satisfies AA^T=E, it is proved that x^TAx=0. If the matrix of order n satisfies A^T=-A, it is proved that x^TAx=0.
- 18. Let a, b be n-dimensional nonzero column vectors, matrix A=2E (N-dimensional)-abt (transposed vector of b) What is the transposition vector of a multiplied by b if the square of A = A +2E
- 19. Given the plane vector a =(2,-2), b =(3,4), a×b=a×c, then the minimum value of |c| is A2B root 2C1/2D root 2/2
- 20. Let X be the normal vector of X plane through three points A (1,2,3) B (2,0,-1) C (3,-2,0) Given X be the normal vector of the X plane through three points A (1,2,3) B (2,0,-1) C (3,-2,0) Given the plane X through three points A (1,2,3) B (2,0,-1) C (3,-2,0) to find the normal vector of X-plane