If all the marbles are identical then order does not matter so you use combination.
nCr so 10C4 = n! / (n-r)!(r!)
Answer:
Step-by-step explanation:
Distribute 4 through the parentheses
Collect like terms
Hope I helped!
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The answer is 3/4 and it was already simplified
Answer:♀️
Step-by-step explanation:
Answer:
A), B) and D) are true
Step-by-step explanation:
A) We can prove it as follows:
B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that . Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then .
C) Consider . This set is orthogonal because , but S is not orthonormal because the norm of (0,2) is 2≠1.
D) Let A be an orthogonal matrix in . Then the columns of A form an orthonormal set. We have that . To see this, note than the component of the product is the dot product of the i-th row of and the jth row of . But the i-th row of is equal to the i-th column of . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then
E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.
In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set and suppose that there are coefficients a_i such that . For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then then .