Answer:
Step-by-step explanation:
The question to be solved is the following :
Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if 
. Recall that given two vectors a,b a⊥ b if and only if 
where 
is the dot product defined in 
. Suposse that 
. We want to find γ such that 
. Given that the dot product can be distributed and that it is linear, the following equation is obtained
Recall that 
are both real numbers, so by solving the value of γ, we get that
By construction, this γ is unique if 
, since if there was a 
such that 
, then
Step-by-step explanation:
Discount amount = discount%of marked price
= 20% of 250
= 20/100x250
=Rs 50
Answer:
The optimal, vertex, value will be a minimum
Step-by-step explanation:
The given zeros of the quadratic relation are 3 and 3
The sign of the second differences of the quadratic relation = Positive
Whereby the two zeros are the same as x = 3, we have that the point 3 is the optimal value or vertex (the repeated point in the graph of the quadratic relation) of the quadratic relation
Whereby, the table of values for the quadratic relation from which the second difference is found starts from x = 3, we have;
To the right of the coordinate points of the zeros of the quadratic relation, the positive second difference in y-values gives as x increases, y increases which gives a positive slope
By the nature of the quadratic graph, the slope of the line to the left of the coordinate point of the zeros of the quadratic relation will be of opposite sign (or negative). The quadratic relation is cup shaped and the zeros, therefore, the optimal value will be a minimum of the quadratic relation
