Simplify the Matrix

Problem

[[35,70,175,140],[40,40,80,80],[40,40,90,70]]*[[2800],[1400],[1500]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 3×4 matrix and the second is a 3×1 vector.

2. Check for compatibility. Matrix multiplication A×B requires the number of columns in A to equal the number of rows in B

3. Conclude that the operation is undefined. The first matrix has 4 columns, but the second matrix has only 3 rows.

4. State the result. Since the dimensions do not match for multiplication (4≠3, the expression cannot be simplified.

Final Answer

[[35,70,175,140],[40,40,80,80],[40,40,90,70]]*[[2800],[1400],[1500]]=Undefined (Dimension Mismatch)

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