Answer:
a. AB: 3 by 7
b. BA: N by N
c. A^TB: N by N
d. BC: 6 by 3
Step-by-step explanation:
Given
Required
The dimension of the following matrices
As a general rule:
For A * B to be successful, the columns in a must equal the rows in B
Using this rule, we have:
So:
The column numbers of B does not equal the row numbers of A.
Hence, BA does not exist
implies that:
If , then
So:
The column numbers of A^T does not equal the row numbers of B.
Hence, does not exist
The number of those who attended the picnic was 8.
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = = 0 where a, b, c, ∈ R and a ≠ 0.
Such questions are best examples of quadratic equations where the unknown is simply assumed to be a variable which when substituted according to the conditions yield a quadratic equation which can easily be solved.
Let x represent the whole population.
Total Spending = Rs. 96
Thus, each individual's contribution is equal to 96/x.
Four people did not show up causing
others to contribute Rs. 4 extra.
So the given condition can be written as
96/(x-4) – 96/x = 4
=>96x – 96(x-4) = 4x(x-4)
=> 96x -96x + 384 = 4x2 – 16x
=> 4x2 – 16x – 384 = 0
=> x2 – 4x – 96 = 0
=> (x – 12)(x + 8) = 0
=> x = 12 or x = -8 (neglect)
So x = 12
x-4 = 8 ( because four of them did not turn up)
∴ The number of those who attended the picnic was 8.
Learn more about quadratic equations here :
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Answer:
<h2>The circumference is multipled by 4.</h2>Step-by-step explanation:
The formula of an area of a circle"
The formula of a circumference of a circle:
The area multipled by 16:
The radius has increased fourfold, therefore:
The circumference is multipled by 4.
You can calculate the area and check the circumference:
Calculate the radius:
<em>divide both sides by π</em>
Calculate the circumference of both circles: