Check the picture below, keeping in mind that opposides sides and interior angles in a parallelogram are congruent.
Maybe write it down, like how you see other math problems.
And then solve it!
:D
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:
length 42 cm and width 26 cm
Step-by-step explanation:
Given
Since Brian tied 136 foot rope around the perimeter , hence perimeter of house is 136 foot.
Given that shape of house is rectangular.
formula to calculate perimeter of rectangle can be used which is 2*(L+B)
where L is length of rectangle and B width of rectangle
Let the L and B be length of rectangular side of house
According to question
length of house is 10 feet less than twice the width of house
mathematically it can be represented as
L = 2*B - 10 --->eq. 1
Perimeter of house = 136 feet
using formula of Perimeter of rectangle
136 = 2*(L+B)
substituting the value of length in terms of width from eq. 1 in formula of perimeter
=> 136/2 = 2*B - 10 + B (2*B+ B = 3B)
=> 68 = 3*B - 10
=> 78 = 3*B
B = 78/3 = 26
Therefore B which is width = 26 CM
length = 2*B - 10= 26*2 - 10 = 52-10=42
length of house = 42 cm
Hence dimension of Brian's house is length 42 cm and width 26 cm
Three hundred forty eight thousand five hundred.
Hope this helps!
