In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. BD
Verified step by step guidance
1
Identify the dimensions of matrices B and D. Matrix B is a 2x3 matrix, and matrix D is a 3x2 matrix.
Check if the matrix multiplication BD is defined. For matrix multiplication to be defined, the number of columns in the first matrix (B) must equal the number of rows in the second matrix (D).
Since B is 2x3 and D is 3x2, the multiplication BD is defined because the number of columns in B (3) matches the number of rows in D (3).
Perform the matrix multiplication by taking the dot product of the rows of B with the columns of D. This will result in a new matrix with dimensions 2x2.
Calculate each element of the resulting matrix by multiplying corresponding elements and summing them up for each position in the new matrix.
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
4m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Matrix Operations
Matrix operations include addition, subtraction, and multiplication, which are fundamental in linear algebra. Each operation has specific rules, such as the requirement for matrices to have compatible dimensions for addition or multiplication. Understanding these operations is crucial for performing calculations and solving problems involving matrices.
The dimensions of a matrix are defined by the number of rows and columns it contains, expressed as 'm x n' where 'm' is the number of rows and 'n' is the number of columns. For matrix multiplication to be defined, the number of columns in the first matrix must equal the number of rows in the second matrix. This concept is essential for determining whether specific matrix operations can be performed.
An operation between matrices is considered defined if the matrices involved meet the necessary conditions for that operation. For example, matrix addition is defined only for matrices of the same dimensions, while multiplication is defined based on the compatibility of the dimensions of the matrices. Identifying whether an operation is defined is critical for correctly solving matrix-related problems.