Final Answer:
For the matrix B=[[3,-1,6],[0,1,4],[5,6,1],[-1,0,7]], the elements are as follows: b₍₁₃₎ = 6, b₍₃₁₎ = 5, and b₍₄₃₎ = 7.
Step-by-step explanation:
Matrix B is a 4x3 matrix with elements represented as b₍ᵢⱼ₎, where ᵢ denotes the row and ⱼ denotes the column. To find b₍₁₃₎, we look at the element in the first row and third column, which is 6. For b₍₃₁₎, we consider the element in the third row and first column, giving us 5. Similarly, for b₍₄₃₎, the element in the fourth row and third column is 7.
Matrix notation provides a concise way to organize and represent data. In this case, the subscripts indicate the position of the element within the matrix. Understanding this notation is fundamental for matrix manipulation and operations. The values of b₍₁₃₎, b₍₃₁₎, and b₍₄₃₎ are determined by their respective positions in the matrix B.
In summary, the values of b₍₁₃₎, b₍₃₁₎, and b₍₄₃₎ in the matrix B=[[3,-1,6],[0,1,4],[5,6,1],[-1,0,7]] are 6, 5, and 7, respectively. This demonstrates how matrix notation allows us to identify and extract specific elements from a given matrix based on their positions.