Simplify the Matrix

Problem

[[0.77,0.23],[0.32,0.68]]*[[0.77,0.23],[0.32,0.68]]

Solution

1. Identify the rule for matrix multiplication, where the element in the ith row and jth column is the dot product of the ith row of the first matrix and the jth column of the second matrix.

2. Calculate the top-left element (a_11) by multiplying the first row by the first column.

(a_11)=(0.77⋅0.77)+(0.23⋅0.32)

(a_11)=0.5929+0.0736=0.6665

3. Calculate the top-right element (a_12) by multiplying the first row by the second column.

(a_12)=(0.77⋅0.23)+(0.23⋅0.68)

(a_12)=0.1771+0.1564=0.3335

4. Calculate the bottom-left element (a_21) by multiplying the second row by the first column.

(a_21)=(0.32⋅0.77)+(0.68⋅0.32)

(a_21)=0.2464+0.2176=0.464

5. Calculate the bottom-right element (a_22) by multiplying the second row by the second column.

(a_22)=(0.32⋅0.23)+(0.68⋅0.68)

(a_22)=0.0736+0.4624=0.536

Final Answer

[[0.77,0.23],[0.32,0.68]]*[[0.77,0.23],[0.32,0.68]]=[[0.6665,0.3335],[0.464,0.536]]

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