Math Problem Statement
सारिणिक | a h g | h b f | g f c | का मान ज्ञात करें।
Solution
The image contains a 3x3 determinant matrix in Hindi, where you need to calculate the determinant value of the matrix:
a & h & g \\ h & b & f \\ g & f & c \end{vmatrix}$$ The formula for the determinant of a 3x3 matrix $$\begin{vmatrix} a & h & g \\ h & b & f \\ g & f & c \end{vmatrix}$$ is: $$\text{Determinant} = a(bc - f^2) - h(hc - fg) + g(hf - gb)$$ Expanding each term, you get: 1. $$a \times (bc - f^2)$$ 2. $$-h \times (hc - fg)$$ 3. $$+g \times (hf - gb)$$ By substituting the values for $$a$$, $$h$$, $$g$$, $$b$$, $$f$$, and $$c$$ (if provided), you can find the determinant. Would you like a detailed example calculation or further steps to apply this formula? Here are some related questions to expand your understanding: 1. How is the determinant of a matrix used in solving systems of linear equations? 2. What are the properties of determinants that simplify calculations? 3. How does the determinant change when rows or columns of a matrix are swapped? 4. What is the geometric interpretation of the determinant in 2D or 3D space? 5. How do you find the inverse of a matrix using its determinant? **Tip:** Practice calculating determinants of smaller matrices, like 2x2 matrices, to understand the expansion pattern better.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Determinants
Matrix Algebra
Formulas
Determinant of a 3x3 matrix
Theorems
Determinant Expansion by Minors and Cofactors
Suitable Grade Level
Grade 10-12