Determine if Linear

Problem

x−[[0,11,25,−16],[15,18,17,−1/2]]=[[1,2/7,3/4,6/5],[−1,−4,0,3]]

Solution

1. Identify the type of equation. This is a linear matrix equation of the form x−A=B where x A and B are matrices of the same dimension (2×4.

2. Isolate the variable matrix x by adding matrix A to both sides of the equation.

x=[[1,2/7,3/4,6/5],[−1,−4,0,3]]+[[0,11,25,−16],[15,18,17,−1/2]]

3. Perform matrix addition by adding corresponding elements from each matrix.

(x_1,1)=1+0=1

(x_1,2)=2/7+11=2/7+77/7=79/7

(x_1,3)=3/4+25=3/4+100/4=103/4

(x_1,4)=6/5−16=6/5−80/5=−74/5

(x_2,1)=−1+15=14

(x_2,2)=−4+18=14

(x_2,3)=0+17=17

(x_2,4)=3−1/2=6/2−1/2=5/2

4. Construct the resulting matrix x using the calculated sums.

x=[[1,79/7,103/4,−74/5],[14,14,17,5/2]]

Final Answer

x=[[1,79/7,103/4,−74/5],[14,14,17,5/2]]

Want more problems? Check here!