Explanation

The additive inverse of a matrix A is the matrix which when added to A results in the zero matrix.  

So, additive inverse of matrix A = -A (negate each element).

Given matrix A =  

[ -7  8 ]  

[  6  3 ]

Additive inverse =  

[ 7  -8 ]  

[ -6  -3 ]

Explanation

Let’s break it down from FELLOW = 465531  

We extract the code for each letter:

- F → 4  

- E → 6  

- L → 5  

- L → 5  

- O → 3  

- W → 1

So, ELLOW = 6 5 5 3 1 → 65531

Explanation

5% of 5000 = (5/100) × 5000 = 250  

Salary after deduction = 5000 - 250 = 4750

Explanation

- Cows: 3 × 4 = 12 legs  

- Chickens: 2 × 2 = 4 legs  

- Cats: 6 × 4 = 24 legs  

Total = 12 + 4 + 24 = 40 legs

Explanation

Odd positions (1st, 3rd, 5th):  

17, 51, 3  

- 17 × 3 = 51  

- 51 ÷ 17 = 3  

Pattern: ×3, ÷17

Even positions (2nd, 4th, 6th):  

2, 19, ?

- 19 − 2 = 17  

- So: 2 → +17 → 19  

- 19 → +38 → 57

Seems it's increasing by:  

+17, +38... (difference increasing by 21)

So the 6th number is 57

Explanation

(a² − b²) is a standard algebraic identity known as the difference of squares.

(a² − b²) = (a − b)(a + b)

Explanation

 From trigonometric identity:  

  tanθ = (p/h) ÷ (b/h) = p/b = sinθ / cosθ

Explanation

95, 90, 83, 74, ?

Now check the differences between terms:

- 95 → 90 = -5

- 90 → 83 = -7

- 83 → 74 = -9

The differences are increasing by -2 each time.

So next difference should be -11.

74 - 11 = 63

Explanation

 cosecθ = 1/sinθ

- Direct reciprocal relationship.

Explanation

By definition: cosecθ = 1/sinθ

- So, sinθ = 1/cosecθ