If |2 3 -1| = -106, find the value of x.

Here are the solutions to the problems: 55. If 2 & 3 & -1 \\ 5 & x & 3 \\ -3 & 5 & 2 = -106 find the value of x. Step 1: Expand the determinant. 2(x · 2 - 3 · 5) - 3(5 · 2 - 3 · (-3)) + (-1)(5 · 5 - x · (-3)) = -106 Step 2: Simplify the expression. 2(2x - 15) - 3(10 + 9) - 1(25 + 3x) = -106 4x - 30 - 3(19) - 25 - 3x = -106 4x - 30 - 57 - 25 - 3x = -106 Step 3: Combine like terms. (4x - 3x) + (-30 - 57 - 25) = -106 x - 112 = -106 Step 4: Solve for x. x = -106 + 112 x = 6 The correct option is A. The value of x is 6. 56. Solve the equation 2x^2 - 32 = 0. Step 1: Isolate the x^2 term. 2x^2 = 32 Step 2: Divide by 2. x^2 = (32)/(2) x^2 = 16 Step 3: Take the square root of both sides. x = ±sqrt(16) x = ± 4 The correct option is B. The solutions are x = 4 or x = -4. 57. Find the sum and the product of the roots of the equation 3x^2 - 2x - 6 = 0 respectively. Step 1: Identify the coefficients a, b, c from the quadratic equation ax^2 + bx + c = 0. For 3x^2 - 2x - 6 = 0, we have a = 3, b = -2, c = -6. Step 2: Calculate the sum of the roots using the formula -(b)/(a). Sum of roots = -(-2)/(3) = (2)/(3) Step 3: Calculate the product of the roots using the formula (c)/(a). Product of roots = (-6)/(3) = -2 The correct option is B. The sum of the roots is (2)/(3) and the product of the roots is -2. 58. Given that P = -2 & 1 \\ 3 & 4 and Q = 5 & -3 \\ 2 & -1 , find the value of 2P + Q. Step 1: Calculate 2P by multiplying each element of matrix P by 2. 2P = 2 -2 & 1 \\ 3 & 4 = 2 × (-2) & 2 × 1 \\ 2 × 3 & 2 × 4 = -4 & 2 \\ 6 & 8 Step 2: Add matrix 2P and matrix Q by adding their corresponding elements. 2P + Q = -4 & 2 \\ 6 & 8 + 5 & -3 \\ 2 & -1 2P + Q = -4 + 5 & 2 + (-3) \\ 6 + 2 & 8 + (-1) Step 3: Perform the addition. 2P + Q = 1 & -1 \\ 8 & 7 The correct option is E. The value of 2P + Q is 1 & -1 \\ 8 & 7 . Send me the next one 📸