It seems like you're working with matrices, but your notation appears slightly unclear. Let me clarify and interpret what you might be asking.

- You’ve given two matrices (or arrays):
  - \( A = [19, 49] \) (likely a row vector or a 1x2 matrix).
  - \( B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \) (a 2x3 matrix).

Now, you asked to "find \( C \)." Without further context, one reasonable interpretation is that you want to perform a matrix operation between \( A \) and \( B \), possibly a multiplication. Here are a few common options:

1. **Matrix multiplication**:
   - For \( A \) to multiply with \( B \) (as \( A \times B \)), the inner dimensions must match.
     - \( A \) is 1x2 and \( B \) is 2x3, so multiplication is possible and will result in a 1x3 matrix.
   
   If this is what you're asking, let's compute the matrix multiplication:

\[
C = A \times B = [19, 49] \times \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}
\]

\[
C = [19(1) + 49(4), 19(2) + 49(5), 19(3) + 49(6)]
\]

\[
C = [19 + 196, 38 + 245, 57 + 294]
\]

\[
C = [215, 283, 351]
\]

Thus, \( C = [215, 283, 351] \).

---

Would you like further details or clarification on any of the steps? Here are a few related questions to consider:

1. What is the difference between matrix multiplication and element-wise multiplication?
2. How do you determine if two matrices are conformable for multiplication?
3. Can you multiply any two matrices of different sizes?
4. What are the properties of matrix multiplication (associative, distributive, etc.)?
5. What applications of matrix multiplication exist in fields like physics or economics?

**Tip**: Always ensure the inner dimensions of matrices align before attempting matrix multiplication!

This guide walks through how to perform matrix multiplication between a 1x2 matrix and a 2x3 matrix. Learn step-by-step how to calculate the resulting matrix using linear algebra concepts, including key formulas and the matrix multiplication conformability theorem. Suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation