Included PDF as well.3.The required matrix is:−0.5 0.25 0[ 0−0.5 0]0014.1. Looking at the original transformations, describing them as matrices for knowntransformations (such as translation, reflection, scale, shear, etc.), composing thetransformations and then inverting them to find the reverse transformation.Details:Let us name the three states 1,2,3 such that 𝐓𝐁 = 𝐓𝟏→𝟐 , 𝐓𝐂 = 𝐓𝟐→𝟑 and 𝐓? = 𝐓𝟑→𝟏 ,where 𝐓𝐁 , 𝐓𝐂 and 𝐓? are the transformation matrices representingtransformation 𝐵 from 1 to 2, transformation 𝐶 from 2 to 3 and the unknowntransformation from 3 to 1 respectively.Since linear transformations are composable, we have:𝐓? ⋅ 𝐓𝐂 ⋅ 𝐓𝐁 = 𝐓𝟑→𝟏 ⋅ 𝐓𝟐→𝟑 ⋅ 𝐓𝟏→𝟐 = 𝐓𝟏→𝟏 = 𝐈The product 𝐓? ⋅ 𝐓𝐂 ⋅ 𝐓𝐁 is equal to 𝐓𝟏→𝟏 , which is equal to the identity matrix 𝐈, since itmaps a state onto itself. Hence, we have:𝐓? ⋅ 𝐓𝐂 ⋅ 𝐓𝐁 = 𝐈Using the distributive property of matrix multiplication:𝐓? ⋅ (𝐓𝐂 ⋅ 𝐓𝐁 ) = 𝐈Using the definition of an inverse:𝐓? ⋅ 𝐓?−𝟏 = 𝐈𝐓? ⋅ (𝐓𝐂 ⋅ 𝐓𝐁 ) = 𝐓? ⋅ 𝐓−𝟏?By compa…
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