Question

Разложите вектор a(3; 1;8) по трем векторам n{0; 1;3) m(1;2;-1), p(2; 0;=1) ​ Смотреть ответ ansfesf ansfesf Ответ:Написать разложение вектора а{3;1;8} по векторам р{0;1;3} , q{1;2;-1},  r{2;0;-1}. а=А р+В q+Сr,   где А,В,С-коэффициенты,  р,q, r вектора. Х :  3=А*0+В*1+С*2,     3=В+2С или  В=3-2С ; У  : 1=А*1+В*2+0*С,      1=А+2В    или  1=А+6-4С    или  А=4С-5; Z   :8=3А-1В-1С  ,           8=3(4С-5)-1(3-2С)-1С  или  С=2. В=3-2С  ⇒     В=3-4=-1; А=4С-5  ⇒     А=8-5=3.   а=3 р-q+2 r Объяснение:v

Answer 1

Vector Decomposition

To decompose the vector a(3; 1; 8) into three vectors n(0; 1; 3), m(1; 2; -1), and p(2; 0; 1), we need to find the coefficients A, B, and C such that a = A * n + B * m + C * p.

Let's solve for A, B, and C step by step:

1. Solve for A: - The x-component equation: 3 = A * 0 + B * 1 + C * 2 - Simplifying the equation: 3 = B + 2C - From this equation, we can solve for B in terms of C: B = 3 - 2C. 2. Solve for B: - The y-component equation: 1 = A * 1 + B * 2 + C * 0 - Simplifying the equation: 1 = A + 2B - Substituting the value of B from the previous step: 1 = A + 2(3 - 2C) - Simplifying further: 1 = A + 6 - 4C - Rearranging the equation: A = 4C - 5.

3. Solve for C: - The z-component equation: 8 = A * 3 - B * 1 + C * 1 - Simplifying the equation: 8 = 3A - B + C - Substituting the values of A and B from the previous steps: 8 = 3(4C - 5) - (3 - 2C) + C - Simplifying further: 8 = 12C - 15 - 3 + 2C + C - Combining like terms: 8 = 15C - 18 - Solving for C: C = 2.

4. Substitute the value of C into the equations for A and B to find their values: - A = 4C - 5 = 4(2) - 5 = 3. - B = 3 - 2C = 3 - 2(2) = -1.

Therefore, the vector a(3; 1; 8) can be decomposed as a = 3n - m - p + 2r, where r is a vector with components (2; 0; -1).

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