Explanation

A matrix with all elements equal to zero is called a Zero Matrix.

Explanation

Transpose of a matrix means converting rows into columns.

Given matrix A:  

[ 1   8

  9   2 ]

Transpose Aᵗ:  

[ 1   9

  8   2 ]

Explanation

Given the operation:

a * b = (2b - a) / b

Let's calculate 2 * 10:

2 * 10 = (2(10) - 2) / 10

= (20 - 2) / 10

= 18 / 10

Simplifying the fraction by dividing both numerator and denominator by 2:

= 9 / 5

Explanation

Given equations:

p - 2q = 14 ... (1)

3p + q = 11 ... (2)

Multiplying equation (2) by 2:

6p + 2q = 22 ... (3)

Adding equation (1) and equation (3):

(p - 2q) + (6p + 2q) = 14 + 22

7p = 36

p = 36/7

Explanation

Given equations:

m + n = 5 ... (1)

2m + 3n = 15 ... (2)

Multiplying equation (1) by 2:

2m + 2n = 10 ... (3)

Subtracting equation (3) from equation (2):

(2m + 3n) - (2m + 2n) = 15 - 10

n = 5

Substituting n = 5 in equation (1):

m + 5 = 5

m = 0

Now, m - n = 0 - 5 = -5

Explanation

The equation is x³ - 4 = 0.

x³ = 4

x = ∛4

x = ∛(2²) = 2^(2/3) ≈ 1.587

There is one real solution.

Explanation

Let's solve for z:

2z/2 + 3z/2 + 4z/2 = 27

Combine like terms:

(2z + 3z + 4z) / 2 = 27

9z / 2 = 27

Multiply both sides by 2:

9z = 54

Divide by 9:

z = 54 / 9

z = 6

Explanation

Ali's current age is x - y.

After y years, his age will be (x - y) + y = x.

Explanation

Solve:

 6x + 11 = 41 ⟹ 6x = 30 ⟹ x = 5

Now, 2x + 3 = 2(5) + 3 = 13

Explanation

Given:

Average of x + 3, x + 6, and x + 9 is 0

((x + 3) + (x + 6) + (x + 9)) / 3 = 0

Combine like terms:

(3x + 18) / 3 = 0

Multiply both sides by 3:

3x + 18 = 0

Subtract 18 from both sides:

3x = -18

Divide by 3:

x = -6