AMTH 106 Lecture 5: AMTH 106_ Ch. 2 Sect. 2.1 Class Lesson 5 Notes

Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as indicated. 3) Find the echelon form of the given matrix. [1 -3 2 4 -11 2 -2 9 5 3 -5 -1] A) [1 0 0 4 1 0 -2 3 27 3 4 17] B) [1 0 0 4 1 -6 -2 3 9 3 4 -7] C) [1 0 0 4 1 0 -2 3 27 3 4 0] D) [1 0 0 4 1 0 -2 3 15 3 4 -1] Solve the problem. 4) Let a_1 = [3 4 -4], a_2 = [-4 1 1], and b = [2 -10 6]. Determine whether b can be written as a linear combination of a_1 and a_2. In other words, determine whether we x_1 and x_2 exist, such that x_1 a_1 + x_2 a_2 = b. Determine the weights x_1 and x_2 if possible. A) x_1 = -1, x_2 = -3 B) x_1 = -2, x_2 = -2 C) x_1 = -2, x_2 = -1 D) No solution

Solve the following equations. Remember that equations may have no solution or many solutions. 2x + 3x + 5(2x - 3) = 30 4x^2 + 7x - 2x (2x - 5) = 17 (x - 2) (x + 4) = 0 (x - 2) (x + 4) = 2x. (x - 2) (x + 4) = -8 x(x - 2) (x + 4) = 0 4x(x - 2) (x - 2) = 0 (y + 2) - 2y (x + 2) = 0 (x + 2) (y + 2) = 0 (x + 2) (y + 21) + (x - 3) (y + 2) = 0 (x - 2) (x + 4) - 2 (x - 4) = 0 (x + 2)^2 + (x - 2)^2 = 0 (x + 2)^2 - (x - 2)^2 = 0 x(x^2 + 2) = 0 x/3 - x/2 = 2/3 x/3 = 2x 2/x - 3/2x = 1 4x(x -4) (x + 3.8)/x^4 - 4x^+ 7x^2 - 5x + 102 = 0 (-12P/P) (3P/2 + P/2) = 480 2/Q = 0 (25/x)/x = 1 (5Q/P + 1)/(1/P + 2) = 20 10 - 1/10Q = 0 4x + 8(x - 2) = 12 2/x = 4 2 - 0.75x = x - 1.5 3x(x - 2) = 0 (x - 2)^2 = 4 100(1 - x) (1 + x) = 0 100(1 - x) (1 + x) = 100 1 - 3/5 + 2/x - = 3/10 7/2x - x/9 = x Refer in exchange rates given in Table 1.1 to answer question 34 to 40. Given answer correct to two decimal places. Am at 400 Canadian Calculate the price of the How many U

Is the vector y =(4 2 0 -3) a linear combination of the vectors v_1=(1 0 1 1), v_2 = (1 3 2 1), v_3=(2 -1 -3 -5), and v_4=(-1 4 5 6)? If yes, exhibits y as a linear combination of the v_i, If no, explain why.