Simplify the Matrix 2A+4B[[3,9],[8,9]][[9,4],[4,0]]

Problem

2*[[3,9],[8,9]]+4*[[9,4],[4,0]]

Solution

1. Identify the matrices A and B from the given expression.

A=[[3,9],[8,9]]

B=[[9,4],[4,0]]

2. Perform scalar multiplication on matrix A by multiplying every entry by 2

2*A=[[2*(3),2*(9)],[2*(8),2*(9)]]

2*A=[[6,18],[16,18]]

3. Perform scalar multiplication on matrix B by multiplying every entry by 4

4*B=[[4*(9),4*(4)],[4*(4),4*(0)]]

4*B=[[36,16],[16,0]]

4. Add the resulting matrices by summing the corresponding entries.

2*A+4*B=[[6+36,18+16],[16+16,18+0]]

2*A+4*B=[[42,34],[32,18]]

Final Answer

2*[[3,9],[8,9]]+4*[[9,4],[4,0]]=[[42,34],[32,18]]

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