Question

Prove that two successive scaling are multiplicative

Answer 1

successive means +1 in that particular number

Answer 2

To prove that two successive scaling are multiplicative

Explanation:

• The resulting matrix in this example shows that successive scaling operations are multiplicative.
• That is, if we were to triple the size of an object two times in succession, the final size could be 9 times that of the original.

For example let's take the product of  successive multiplies of 5 is 300 Determine the multiplies

For this

Let x ,y → x, y are multiple of 5

5m₁ = x , 5m₂ = y

x , y  are successive

m₂ = m₁ + 1

5m₁ × 5m₂ = 300      --1

5 × 5 [ m₁ [ m₁ + 1 ]] = 300

m₁² + m₁ -12 = 0

m₁² + 4m₁ - 3m₁ - 12 = 0

m₁ [ m₁ + 4] - 3 [ m₁ + 4 ] = 0

[m₁ - 3] [m₁ + 4] = 0

m₁ = 3 , m₂ = -4

Now

5 × 3 , 5 × 4       = 300       ----2

5 × -4 , 5 × -3     = 300      ------3

Both have the same result

∴Hence proved two successive scaling are multiplicative