Step-by-step explanation:
This isn't. a true identity.
The standard form: Ax + By = C
y = 90 - 15x <em>add 15x to both sides</em>
<h3>15x + y = 90</h3>
<u>well 8 divided by 4 is 2 and 11-8+2 is 5 and 5 times 4 is 20 so 20 is the answer
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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 .
Answer: 4 and 7.5 you multiply them
Step-by-step explanation: