Use Cramer's rule to solve the system. 3x + 4z = 0 3x + 2y = 24 -y + 4z = -36 Let A be the coefficient matrix of the given system of equations. Find the determinants. $|A| = \boxed{\text{ }}, |D_x| = \boxed{\text{ }}, |D_y| = \boxed{\text{ }}, |D_z| = \boxed{\text{ }}$ (Simplify your answers.)
Added by Susan A.
Close
Step 1
The given system of equations can be written in matrix form as: A * X = B where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. The coefficient matrix A is: A = [3 0 4; 3 2 0; 0 -1 4] The variable matrix X is: X = [x; y; Show moreā¦
Show all steps
Your feedback will help us improve your experience
Luke Mullikin and 87 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Write the determinants $D, D_{x}, D_{y},$ and $D_{z}$ for the systems given, then determine if a solution using Cramer's rule is possible by computing the value of $D$ without the use of a calculator (do not solve the system). Try to determine how the system from Part (b) is related to the system in Part (a). a. $\left\{\begin{array}{l}4 x-y+2 z=-5 \\ -3 x+2 y-z=8 \\ x-5 y+3 z=-3\end{array}\right.$ b. $\left\{\begin{array}{l}4 x-y+2 z=-5 \\ -3 x+2 y-z=8 \\ x+y+z=-3\end{array}\right.$
Systems of Equations and Inequalities
Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More
Write the determinants $D, D_{x}, D_{y},$ and $D_{z}$ for the systems given, then determine if a solution using Cramer's rule is possible by computing the value of $D$ without the use of a calculator (do not solve the system). Try to determine how the system from Part (b) is related to the system in Part (a). a. $\left\{\begin{array}{l}2 x+3 z=-2 \\ -x+5 y+z=12 \\ 3 x-2 y+z=-8\end{array}\right.$ b. $\left\{\begin{array}{l}2 x+3 z=-2 \\ -x+5 y+z=12 \\ 3 x-5 y+2 z=-8\end{array}\right.$
Use Cramer's rule and the calculator provided to find the value of x that satisfies the system of linear equations: x - 5y = -4 3x + 2y - 3z = 3 3x + 4y - 3z = -5 The determinant of the coefficient matrix is
Madhur L.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD