Explanation

 A = 1, H = 1 → A + 2 = 7 → A = 5  

If Z = 26, O = 15 → Z - O = 26 - 15 = 11

Explanation

If yesterday was Friday, then today is Saturday.  

- Tomorrow → Sunday  

- Day after tomorrow → Monday

Explanation

- 12 → Even number  

- 20 → Even number  

- 2 → Even number  

- 5 → Odd number

Since 5 is the only odd number, while the rest are even, it does not follow the pattern.

Explanation

63, 48, 35, 15, ?

Now, find the differences between consecutive terms:

- 63 → 48  → −15  

- 48 → 35  → −13  

- 35 → 15  → −20

Wait, something's off. Let's double-check with consistent logic.

Try this:

63 - 15 = 48  

48 - 13 = 35  

35 - 20 = 15

Now we got:

-15, -13, -20 → Pattern doesn't seem linear.

Try checking the alternating pattern:

- 63 → 48 (−15)  

- 48 → 35 (−13)  

- 35 → 15 (−20)  

- 15 → ? (maybe −13 again?)

If the pattern alternates between −15, −13, −20, −13, then:

15 − 13 = 2

Explanation

- (AB)ᵗ = Bᵗ × Aᵗ  

- This is a standard matrix algebra rule

Transpose reverses the order of multiplication  

Example:  

If A = 2×3 matrix, B = 3×2, then:  

(AB)ᵗ = Bᵗ × Aᵗ

Explanation

A matrix B is symmetric if Bᵗ = B  

- This means the elements across the main diagonal are mirrored  

Example:  

Matrix B =  

[1 2]  

[2 3]  

Then Bᵗ =  

[1 2]  

[2 3] ⇒ Same as B ⇒ Symmetric

Explanation

The Addition Property of Equality states: if you add the same number to both sides of an equation, the equality remains unchanged.

Absolute value refers to the distance of a number from zero on the number line, always positive.  

Explanation

 Natural Numbers:

These are the counting numbers starting from 1 (i.e., 1, 2, 3, 4, ...).

The given set S = {1, 2, 3, 4} exactly fits this definition.

- Whole Numbers:

Whole numbers start from 0 (i.e., 0, 1, 2, 3, 4, ...).

Since 0 is missing in the set, it's not a set of whole numbers.

- Prime Numbers:

Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves.

In this set:

  - 1 is not a prime number,

  - 4 is not a prime number (4 is divisible by 2).

  So it's not a set of primes.

- Even Numbers:

Even numbers are divisible by 2. In the set:

Only 2 and 4 are even; 1 and 3 are odd.

 So it’s not a set of even numbers either.

Explanation

Matrices do not obey the Commutative Law of Multiplication; for matrices A and B, AB is generally not equal to BA, unlike with regular numbers.

While both matrix addition and scalar multiplication of matrices follow commutative and associative laws,

The commutative law does not hold for matrix multiplication. 

Explanation

Two angles are called complementary when their measures add up to 90 degrees.

Two angles are called supplementary when their measures add up to 180 degrees.