question 30 points 2

consider the system of equations. find the determinant value of the matrix of the coefficients of the variables.

$x + y + z = 4$
$4x + 3y + 3z = 6$
$3y + 3z - 4x = 9$

$|a| = 6$
$|a| = 7$

Question

question 30 points 2

consider the system of equations. find the determinant value of the matrix of the coefficients of the variables.

$x + y + z = 4$
$4x + 3y + 3z = 6$
$3y + 3z - 4x = 9$

$|a| = 6$
$|a| = 7$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Coefficient Matrix", "Matrix Determinant" ], "new_concepts": [], "current_concepts": [ "Coefficient Matrix", "Matrix Determinant", "System of Linear Equations" ] } ## Rearrange the system of equations Using the *Coefficient Matrix* knowledge point $$ \begin{aligned} x + y + z &= 4 \ 4x + 3y + 3z &= 6 \ -4x + 3y + 3z &= 9 \end{aligned} $$ ## Construct the coefficient matrix Using the *Coefficient Matrix* knowledge point $$ A = \begin{pmatrix} 1 & 1 & 1 \ 4 & 3 & 3 \ -4 & 3 & 3 \end{pmatrix} $$ ## Calculate the determinant of the matrix Using the *Matrix Determinant* knowledge point $$ \begin{aligned} |A| &= 1 \cdot \begin{vmatrix} 3 & 3 \ 3 & 3 \end{vmatrix} - 1 \cdot \begin{vmatrix} 4 & 3 \ -4 & 3 \end{vmatrix} + 1 \cdot \begin{vmatrix} 4 & 3 \ -4 & 3 \end{vmatrix} \ &= 1 \cdot (9 - 9) - 1 \cdot (12 - (-12)) + 1 \cdot (12 - (-12)) \ &= 0 - 24 + 24 \ &= 0 \end{aligned} $$

(A) $|A| = 6$

(B) $|A| = 7$

(C) $|A| = 10$

(D) $|A| = 13$

(E) $|A| = 0$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Matrix Determinant" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Rearrange the system of equations

Construct the coefficient matrix

Calculate the determinant of the matrix

Answer: