Calculate the determinant of the given matrix.

April 12, 2026Mathematics

ScanSolve AI Answer

April 12, 2026

Answer

Step 1: Calculate the determinant of the given matrix. The determinant of a $2 \times 2$ matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is given by $ad - bc$ . For the given matrix $\begin{bmatrix} y-1 & 2 \\ 4 & 3 \end{bmatrix}$ , the determinant is: $(y-1)(3) - (2)(4)$

Step 2: Set the determinant equal to $4$ as given in the problem. $3(y-1) - 8 = 4$

Step 3: Expand and simplify the equation. $3y - 3 - 8 = 4$ $3y - 11 = 4$

Step 4: Solve for $y$ . Add $11$ to both sides of the equation: $3y = 4 + 11$ $3y = 15$ Divide by $3$ : $y = \frac{15}{3}$ $y = 5$

The value of $y$ is: $5$ Send me the next one 📸

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Calculate the determinant of the given matrix. The determinant of a 2 × 2 matrix a & b \\ c & d is given by ad - bc.

Asked on April 12, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 12, 2026

Step 1: Calculate the determinant of the given matrix. The determinant of a 2 × 2 matrix a & b \\ c & d is given by ad - bc. For the given matrix y-1 & 2 \\ 4 & 3 , the determinant is: (y-1)(3) - (2)(4) Step 2: Set the determinant equal to 4 as given in the problem. 3(y-1) - 8 = 4 Step 3: Expand and simplify the equation. 3y - 3 - 8 = 4 3y - 11 = 4 Step 4: Solve for y. Add 11 to both sides of the equation: 3y = 4 + 11 3y = 15 Divide by 3: y = (15)/(3) y = 5 The value of y is: 5 Send me the next one 📸