https://file.aiquickdraw.com/mathbot/file/1726799219587sip9c3gy.jpg

Let's go through the questions in the image step by step:

### 1. Solve for \( q \):

The equation given is:

\[
\begin{pmatrix} 6 \\ 3q \end{pmatrix} = \left( \begin{pmatrix} q \\ 1 \end{pmatrix} + \frac{1}{15} \begin{pmatrix} 8 \\ 4 \end{pmatrix} \right)
\]

We need to equate components to solve for \( q \).

### 2. Matrix multiplication:

You are asked to find the order of the product of two matrices:

\[
\begin{pmatrix} 1 & -7 \\ 5 & 9 \end{pmatrix} \times \begin{pmatrix} 5 & -3 & 8 \\ 0 & 2 & -1 \end{pmatrix}
\]

To determine the order of the result, we need to calculate the product and identify the dimensions.

### 3. Singular matrix condition:

Given matrix \( A = \begin{pmatrix} 4 & -6 \\ x & 3 \end{pmatrix} \), we are asked to find \( x \) such that the matrix is singular (determinant = 0).

### 4. Matrix equation:

Solve the matrix equation:
\[
\begin{pmatrix} 3 & 6 \\ 0 & -4 \end{pmatrix} \begin{pmatrix} 1 \\ 5 \end{pmatrix} = \begin{pmatrix} 33 & -12 \\ -20 & -16 \end{pmatrix}
\]

### 5. Solve for \( z \):

Given:
\[
\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 2 & 1 \\ 0 & 2 \end{pmatrix} \begin{pmatrix} 3 \\ 2 \end{pmatrix} + \begin{pmatrix} 4 \\ 1 \end{pmatrix}
\]

and \( z = x - y \), find the value of \( z \).

---

Would you like me to solve one of these questions in more detail?

Solve the following math problems: 1. Find the value of q. 2. Determine the order of the product of two matrices. 3. Given a matrix A, find the value of x for which the matrix is singular. 4. Solve the matrix equation to find x. 5. Solve for z, given a system of equations with matrices.

This exercise covers key topics in matrix operations, including finding the order of a product of matrices, solving for unknowns in matrix equations, and identifying singular matrices. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation