Simplify the Matrix [[1,2,3,4,5,6,7],[0,3,8,15,24,35,48]]*6

Problem

6⋅[[1,2,3,4,5,6,7],[0,3,8,15,24,35,48]]

Solution

1. Identify the operation as scalar multiplication of a 2×7 matrix by the constant 6

2. Apply the rule for scalar multiplication, which requires multiplying every individual element within the matrix by 6

3. Calculate the products for the first row: 6⋅1=6 6⋅2=12 6⋅3=18 6⋅4=24 6⋅5=30 6⋅6=36 and 6⋅7=42

4. Calculate the products for the second row: 6⋅0=0 6⋅3=18 6⋅8=48 6⋅15=90 6⋅24=144 6⋅35=210 and 6⋅48=288

5. Construct the resulting matrix using the calculated values.

Final Answer

6⋅[[1,2,3,4,5,6,7],[0,3,8,15,24,35,48]]=[[6,12,18,24,30,36,42],[0,18,48,90,144,210,288]]

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