Q40. Solve聽det4x鈭�2鈭抶鈭�31鈭�623=... [FREE SOLUTION]

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Chapter 4: Q40. (page 186)

Solve $\det [\begin{matrix} 4 & x & 鈭� 2 \\ 鈭� x & 鈭� 3 & 1 \\ 鈭� 6 & 2 & 3 \end{matrix}] = 鈭� 3$ for x.

Short Answer

Expert verified

The value of $x = \frac{5}{3}, 鈥� x = - 1$ .

Step by step solution

- Calculate the determinant

Find the determinant in this case by using expansion by minors.

$\begin{matrix} \det [\begin{matrix} 4 & x & 鈭� 2 \\ 鈭� x & 鈭� 3 & 1 \\ 鈭� 6 & 2 & 3 \end{matrix}] = 鈭� 3 \\ 4 |\begin{matrix} 鈭� 3 & 1 \\ 2 & 3 \end{matrix}| 鈭� x |\begin{matrix} 鈭� x & 1 \\ 鈭� 6 & 3 \end{matrix}| + (鈭� 2) |\begin{matrix} 鈭� x & 鈭� 3 \\ 鈭� 6 & 2 \end{matrix}| = 鈭� 3 \end{matrix}$

- Evaluate 2×2 determinants

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is., $|\begin{matrix} a & b \\ c & d \end{matrix}| = a d 鈭� b c$ .Apply this definition to find the $2 脳 2$ determinant.

$\begin{matrix} 4 |\begin{matrix} 鈭� 3 & 1 \\ 2 & 3 \end{matrix}| 鈭� x |\begin{matrix} 鈭� x & 1 \\ 鈭� 6 & 3 \end{matrix}| + (鈭� 2) |\begin{matrix} 鈭� x & 鈭� 3 \\ 鈭� 6 & 2 \end{matrix}| = 鈭� 3 \\ 4 (鈭� 3 (3) 鈭� 2 (1)) 鈭� x (鈭� x (3) 鈭� (鈭� 6)) 鈭� 2 (鈭� x (2) 鈭� (鈭� 3) (鈭� 6)) = 鈭� 3 \\ 4 (鈭� 9 鈭� 2) 鈭� x (鈭� 3 x + 6) 鈭� 2 (鈭� 2 x 鈭� 18) = 鈭� 3 \end{matrix}$

- Solve for x

Further simplify the values.

$\begin{matrix} 4 (鈭� 9 鈭� 2) 鈭� x (鈭� 3 x + 6) 鈭� 2 (鈭� 2 x 鈭� 18) = 鈭� 3 \\ 4 (鈭� 11) 鈭� x (鈭� 3 x) 鈭� x (6) 鈭� 2 (鈭� 2 x) 鈭� 2 (鈭� 18) = 鈭� 3 \\ 鈭� 44 + 3 x^{2} 鈭� 6 x + 4 x + 36 = 鈭� 3 \\ 3 x^{2} 鈭� 2 x 鈭� 5 = 0 \\ 3 x^{2} + 3 x 鈭� 5 x 鈭� 5 = 0 \\ 3 x (x + 1) 鈭� 5 (x + 1) = 0 \\ (3 x 鈭� 5) (x + 1) = 0 \\ x = \frac{5}{3}, 鈥� x = 鈭� 1 \end{matrix}$

Therefore, possible values for x are $x = \frac{5}{3}, 鈥� x = - 1$ .

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Solve $\det [\begin{matrix} 4 & x & 鈭� 2 \\ 鈭� x & 鈭� 3 & 1 \\ 鈭� 6 & 2 & 3 \end{matrix}] = 鈭� 3$ for x.

Short Answer

Step by step solution

- Calculate the determinant

- Evaluate 2×2 determinants

- Solve for x

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91影视

Solvedet4x鈭�2鈭�x鈭�31鈭�623=鈭�3for x.

Short Answer

Step by step solution

- Calculate the determinant

- Evaluate 2×2 determinants

- Solve for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Decision Maths

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve $\det [\begin{matrix} 4 & x & 鈭� 2 \\ 鈭� x & 鈭� 3 & 1 \\ 鈭� 6 & 2 & 3 \end{matrix}] = 鈭� 3$ for x.