Math Problem Statement
, C = "0 1 4# −4 −1 2 what is -2C^T
Solution
Let's break down the problem step by step:
You provided the matrix :
0 & 1 & 4 \\ -4 & -1 & 2 \end{bmatrix}$$ ### Step 1: Find the transpose of matrix $$C$$ (denoted as $$C^T$$). The transpose of a matrix is obtained by swapping rows and columns. So the transpose of $$C$$, which is a $$2 \times 3$$ matrix, will become a $$3 \times 2$$ matrix: $$C^T = \begin{bmatrix} 0 & -4 \\ 1 & -1 \\ 4 & 2 \end{bmatrix}$$ ### Step 2: Multiply the transpose $$C^T$$ by $$-2$$. Now we need to multiply each element of $$C^T$$ by $$-2$$: $$-2C^T = -2 \times \begin{bmatrix} 0 & -4 \\ 1 & -1 \\ 4 & 2 \end{bmatrix} = \begin{bmatrix} 0 & 8 \\ -2 & 2 \\ -8 & -4 \end{bmatrix}$$ ### Final Answer: $$-2C^T = \begin{bmatrix} 0 & 8 \\ -2 & 2 \\ -8 & -4 \end{bmatrix}$$ Would you like any further details on the steps? --- Here are five related questions you might find interesting: 1. What is the determinant of a square matrix and how do you calculate it? 2. How do you multiply two matrices together? 3. What is the inverse of a matrix, and how is it computed? 4. Can you explain the significance of matrix transposition in geometry? 5. How do eigenvalues and eigenvectors relate to matrix transformations? **Tip:** When multiplying matrices by a scalar, every element in the matrix is scaled by the same factor, but the overall structure of the matrix remains the same.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Operations
Matrix Transposition
Scalar Multiplication
Formulas
Matrix Transposition
Scalar Multiplication Formula: kA = k * A_ij
Theorems
Matrix Transposition Properties
Scalar Multiplication of Matrices
Suitable Grade Level
Grades 10-12