Math Problem Statement
El valor del K que hace que el determinante de la matriz sea 0 es:
Solution
The problem asks to find the value of that makes the determinant of the given matrix equal to zero.
The matrix is:
3 & k \\ 1 & 5 \end{pmatrix}$$ The determinant of a $$2 \times 2$$ matrix $$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$ is calculated as: $$\text{Determinant} = ad - bc$$ For the given matrix, this becomes: $$\text{Determinant} = (3 \times 5) - (k \times 1) = 15 - k$$ To make the determinant equal to zero, we set the equation: $$15 - k = 0$$ Solving for $$k$$: $$k = 15$$ Thus, the value of $$k$$ that makes the determinant zero is $$\boxed{15}$$. Would you like further explanation or details on how the determinant is calculated? Here are 5 related questions to deepen your understanding: 1. How do you calculate the determinant of a $$3 \times 3$$ matrix? 2. What does it mean geometrically when the determinant of a matrix is zero? 3. How do determinants help in solving systems of linear equations? 4. What is the importance of the sign of a matrix's determinant? 5. How would the solution change if the matrix size increased? **Tip:** In higher dimensions, a zero determinant indicates that the matrix is singular and non-invertible.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Determinants
Matrices
Linear Algebra
Formulas
Determinant of 2x2 matrix: ad - bc
Theorems
Determinant Theorem
Suitable Grade Level
Grades 9-12