Math Problem Statement

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Solution

The second question from your problem set is as follows:

Problem: Identify w,x,y,zw, x, y, z in the equation:

w & z \\ y & x \end{pmatrix} + \begin{pmatrix} 3 & 4 \\ 2 & 6 \end{pmatrix} = \begin{pmatrix} w+z & z+4 \\ y+2 & x+6 \end{pmatrix} = \begin{pmatrix} 3 & 4 \\ 2 & 6 \end{pmatrix}$$ **Solution:** From the given equation, compare the elements of the matrices on both sides. 1. For the first row, first column: $$w + z = 3$$ 2. For the first row, second column: $$z + 4 = 4$$ Solving for $$z$$: $$z = 0$$ Substitute $$z = 0$$ into the first equation: $$w + 0 = 3 \implies w = 3$$ 3. For the second row, first column: $$y + 2 = 2$$ Solving for $$y$$: $$y = 0$$ 4. For the second row, second column: $$x + 6 = 6$$ Solving for $$x$$: $$x = 0$$ Thus, the values are: - $$w = 3$$ - $$x = 0$$ - $$y = 0$$ - $$z = 0$$ --- Would you like further details on how to approach such problems? Here are some related questions: 1. What is a matrix and how do we add two matrices? 2. How do you perform matrix multiplication? 3. What are the types of matrices, such as symmetric and skew-symmetric matrices? 4. What is the role of determinants in solving systems of equations? 5. How can elementary row transformations help find the inverse of a matrix? **Tip:** Always check matrix dimensions before performing operations like addition or multiplication to ensure they are valid.

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Math Problem Analysis

Mathematical Concepts

Matrix Addition
Linear Equations

Formulas

Matrix addition rule: A + B = C where corresponding elements of matrices are added.
System of linear equations for solving variables in matrices.

Theorems

Matrix Addition Theorem

Suitable Grade Level

Undergraduate (First Year)