When multiplying matrices A (order m × n) and B (order n × p), the resulting matrix has an order of m × p.
Given:
x ∝ 1/y
y ∝ 1/z
We can rewrite these proportions as:
x = k₁/y (where k₁ is a constant)
y = k₂/z (where k₂ is a constant)
Substitute the expression for y into the first equation:
x = k₁/(k₂/z)
Simplify:
x = k₁z/k₂
x ∝ z
The Laplace equation is a 2nd order partial differential equation, given by:
∇²u = 0 or ∂²u/∂x² + ∂²u/∂y² + ∂²u/∂z² = 0
In an arithmetic progression, the sum of n terms between a and b is given by: Sum = n(a+b)/2
This formula uses the first and last terms to find the total of evenly spaced values.
To find the sum, we need to calculate each term:
i^101 = i (since i^1 = i and the powers repeat every 4 terms)
i^102 = i^2 = -1
i^103 = i^3 = -i
i^104 = i^4 = 1
Now, let's add them up:
i + (-1) + (-i) + 1 = 0
For matrices A and B, the inverse of the product AB is given by:
(AB)⁻¹ = B⁻¹A⁻¹
The square root of any prime number is not a perfect square.
Therefore, √𝑝 is irrational, meaning it cannot be expressed as a fraction of two integers.
Given y = 2/x
Let's find the first and second derivatives:
dy/dx = -2/x²
d²y/dx² = 4/x³
Now, let's evaluate y + 1/2 * d²y/dx²:
y + 1/2 * d²y/dx² = 2/x + 1/2 * 4/x³
= 2/x + 2/x³
= (2x² + 2)/x³
= 2(x² + 1)/x³
= 2(1 + x²)/x³
The X-axis and Y-axis intersect at the point (0, 0), known as the origin.
It is the central reference point in the coordinate plane.
