Evaluate the following matrix product.

3 −3 −4 −2





−2
1
5
5




=
 

 


Let's evaluate the given matrix product. The matrix multiplication is between a 1x4 row vector \(\mathbf{v} = [3, -3, -4, -2]\) and a 4x1 column vector \(\mathbf{w} = \begin{bmatrix} -2 \\ 1 \\ 5 \\ 5 \end{bmatrix}\).

The general rule for matrix multiplication is:

\[
\mathbf{v} \cdot \mathbf{w} = 3(-2) + (-3)(1) + (-4)(5) + (-2)(5)
\]

Now, let's perform the calculations step by step:

\[
3(-2) = -6
\]
\[
-3(1) = -3
\]
\[
-4(5) = -20
\]
\[
-2(5) = -10
\]

Now, sum all the results:

\[
-6 + (-3) + (-20) + (-10) = -39
\]

Thus, the result of the matrix product is:

\[
\mathbf{v} \cdot \mathbf{w} = -39
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. What are the properties of matrix multiplication?
2. How do you multiply a matrix with different dimensions?
3. Can matrix multiplication result in a matrix of different dimensions than the original?
4. What are some real-world applications of matrix multiplication?
5. How would the result change if one of the elements in the vectors was different?

**Tip**: Always check the dimensions of matrices before multiplying to ensure that the product is defined.

Evaluate the following matrix product.

3 −3 −4 −2





−2
1
5
5



 =

This page provides a detailed explanation of the matrix multiplication between a 1x4 row vector and a 4x1 column vector, resulting in a scalar value of -39. Learn about the properties of matrix multiplication, including the dot product and key theorems, suitable for students in Grades 9-12.

Math Problem Statement

    −2 1 5 5    

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation