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In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article.
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Rm if every vector b in Rm is a linear combination of a 1;;a p (i.e. Spanfa 1;;a pg Rm). Theorem (4) Let A be an m n matrix. Then the following statements are logically equivalent 1 For each b in Rm, the equation Ax b has a solution. 2 Each b in Rm is a linear combination of the columns of A. 3 The columns of A span Rm. However, before we perform multiple linear regression, we must first make sure that five assumptions are met 1. Linear relationship There exists a linear relationship between each predictor variable and the response variable. 2. No Multicollinearity None of the predictor variables are highly correlated with each other.
The expression av bw is called a linear combination of v and w. Using a little linear algebra, you can show linear combinations of more complicated vectors. As an example, the vector (7, 11, 15) is a linear combination of the vectors (1, 1, 1) and (1, 2, 3). The first vector (1, 1, 1) is multiplied by the scalar 3, and the second vector (1, 2. Expert Answer. Which of the following is NOT a linear combination of A(1 3 4 0) and B (2 1 0 2) (3 1 4 4) (2 6 8 1) (1 8 12 2) Consider the points A(2,2,3) and B(1,1,4). Which of the following is a unit vector in the direction of AB (1,1,1) 31 (1,1,1) (1,1,1) 671 (3,3,7) 31 (1,1,1) Question 38 (1.
13) Which of the following sets of constraints results in an unbounded maximization problem A) X Y 100 and X Y 50. B) X Y 15 and X - Y 10. C) X Y 10 and X 5. D) X 10 and Y 20. E) All of the above have a bounded maximum. 14) What is the region that satisfies all of the constraints in linear programming. Which of the following are linear combinations of u (0,2,2) and v (1,3,1) (a) (2,2,2) (b) (0,4,5) (c) (0,0,0) Expert Answer. Who are the experts Experts are tested by Chegg as specialists in their subject area. We review their content and use your feedback to keep the quality high. 100 (1 rating) S View the full answer. Previous question Next question. COMPANY. About Chegg;. is a linear combination of vectors , , , (for any whole number) you will do the following . Step 1 Set up the augmented matrix and row reduce it. Step 2 Use the reduced form of the matrix to determine if the augmented matrix represents a consistent system of equations. If so, then is a linear combination of the others. Otherwise, it is not.