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In isosceles △ ABC, ab = AC, AC side midline BD divides the circumference of triangle into 12cm and 18cm, and calculates the waist length and bottom length of isosceles △ ABC
Let the waist length be 2xcm and the bottom length be YCM. According to the meaning of the title, we can get: 2x + x = 12x + y = 18 or 2x + x = 18x + y = 12. The solution is x = 4Y = 14 or x = 6y = 6, 2x = 8 or 2X = 12, and the side lengths of the two cases satisfy the trilateral relationship, so the bottom and waist of isosceles △ ABC are 14cm, 8cm or 6cm, 12cm respectively
Vector B can be represented linearly by vector groups A1, A2... Am
Vector B can be expressed linearly by vector groups A1, A2... Am, then the following conclusion is correct: 1. There is a group of non-zero numbers K1, K2, K3... Such that B = k1a1 + k2a2 +... + kmam 2. There is a group of non-zero numbers K1, K2,... Km such that the above formula holds 3. The only group of numbers K1, K2... Km such that the above formula holds 4. Vector groups A1, A2, A3,... B are linearly correlated (important reason)
Linear representation: for vector group A1, A2... Am and vector B, if there is a group of numbers K1, K2, K3... Km such that B = k1a1 + k2a2 +... + kmam, then B can be expressed linearly by vector group A1, A2... Am
Given vector group A1, A2 It is proved that vector group B1 = A1, B2 = a1 + A2 ，br=a1+a2+… +AR is also linearly independent
Suppose there is a set of real numbers K1 So that k1b1 + +Krbr = 0, namely & nbsp; & nbsp; k1a1 + K2 (a1 + A2) + +kr（a1+… +ar）=（k1+… +kr）a1+（k2+… +kr）a2+… +Krar = 0. Because vector group A1, A2 So K1 + +kr＝0… KR − 1 + Kr = 0kr = 0. Because of the coefficient matrix of the equations 101… 1 ⋮⋮⋱⋮ 0001. = 1 ≠ 0, so from the necessary and sufficient conditions for the existence of nonzero solutions of homogeneous linear equations, K1 = K2 = =So vector group B1, B2 It is linear independent
RELATED INFORMATIONS
- 1. Let the rank of vector group A1, A2. Am be r, then any r linearly independent vectors in A1, A2,. Am constitute its maximal linearly independent group
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