Explanation

Let's solve the equations:

1. x + y = 5

2. x - y = 3

Add both equations:

2x = 8

x = 4

Now, substitute x = 4 in equation (1):

4 + y = 5

y = 1

The solution is (4, 1).

Explanation

The expression ad - bc is called the Determinant of A, denoted as |A|.

Explanation

If |A| ≠ 0, then matrix A is Non-singular (also known as invertible).

Explanation

The notation n√x^m can be rewritten in power form as:

(x^m)^(1/n) = x^(m/n)

Explanation

Using the change of base formula:

log_b^a / log_b^d = log_d^a

Explanation

Let's expand both expressions:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

Now, add them:

(a + b)² + (a - b)² = a² + 2ab + b² + a² - 2ab + b²

= 2a² + 2b²

Explanation

Let's use the Pythagorean theorem:

Height of pole (perpendicular) = 12m

Length of string (hypotenuse) = 20m

Distance between foot of pole and end point of string (base) = √(hypotenuse² - perpendicular²)

= √(20² - 12²)

= √(400 - 144)

= √256

= 16m

Explanation

Given:

x̄ (mean) = 12

∑x (sum) = 132

The formula for mean is:

x̄ = ∑x / n

Rearrange to find n:

n = ∑x / x̄

= 132 / 12

= 11

Explanation

To solve |3x| = 6:

3x = 6 or 3x = -6

x = 2 or x = -2

Explanation

When multiplying matrices A (order m × n) and B (order n × p), the resulting matrix has an order of m × p.