Which of the following statements about vectors is false? O The scalar multiplication of a vector by n, where n > o, keeps the vector in the same direction O The vector sum of two vectors is called the resultant. O A vector diagram consists of directed line segments. O Two vectors are equal if they have the same magnitude and are in opposite directions. By what approximate scalar amount has vector a been multiplied by to produce vector a? (Diagram drawn to scale) V O -2 O 2 O 4 O -4When the method of substitution is used to solve the system 2.1! 33 i 13th 15 a possible third equation that must be solved is: (:3 EyE(3y;z)=1s (:3 2y3[)=2 {3| 2(21;2)=1 {j 202:\") :i::= 2 Which of the following systems of linear equations has a solution of (3,8}? Consider the matrices below. A = 8 7 If D = C- A, then the element do, is: 0 6 O -2 O -5 O0 Given the matrices below. 7 A B 13 0 If A x B = 2F + 30, then for is: O 16 O 25 O 8 O not possibleFranz has a small wood working shop in his garage where he makes four different kinds of toys: a train (7), an airplane (A), a dragon (D), and a nameplate (N). Each toy is made of either pine or oak. The matrices o and w represent the sales for October and November. T A D N D = Pine 5 0 2 Oak 1 2 1 3 T A D N N= Pine 2 3 Oak 1 0 2 Determine the matrix that represents the total sales for toys sold in October and November. O impossible to solve 2 1 1 [7 7 1 5]Years ago, an investor purchased growth stocks with the expectation that they would increase in value over time. The purchase included 100 shares of stock A, 200 shares of stock B, and 150 shares of stock C. At the end of each year the value of each stock was recorded (see table below). 1984 1985 1986 Stock A 68.00 72.00 75.00 Stock B 55.00 60.00 67.50 Stock C 82.50 84.00 87.00 Create a matrix for the number of shares purchased and one for the value of stocks by year (above) and then use matrix multiplication to calculation the total value of the stock purchases at the end of each year. 32450 O 1 27625 38100 31459 OT= 27555 33270 O T= [31459 27565 33270] O T= [30175 31800 34050]A system of equations is defined by 3x + 4y = - 5 2x + by = - 8 A student sets up the following matrices to solve for matrix x. 4 [2 8] x x = $[=] What is the solution to the system? O ( 1, -2) O (-2, 1 ) O (5, -8) O (4, -3 ) Given the following matrix equation, determine the value of "y" to the nearest tenth. O 35 O 13 O 11 O 12Using matrices, solve the system of linear equations defined by 20 - b - 4c = 3 -a + 36 + c = -10 3a + 26 - 20 = -2 The value of a is O -2 O 2 Oo O -3 Determine the resulting vector when a = (2, -6) is rotated so counter clockwise and increased in size by a multiple of 4. O (-4+6V/3,4V/3+6) O ( 4v/3, 12V/3) O (4v/3 + 12, -8v/3) O ( 4v/3 + 12,4 -12V/3) Reflect @ = (4,-7) over the y-axis and then again over the x-axis, and find the result of the reflected vector. O (-4, 7) O ( 4, - 7) O (7.-4) O (-4, -7)=What is the approximate magnitude and bearing of the vector shown in the diagram below? Scale: 1 inch = 50 mph 1 " 60 -2" -1" 0 -1" - O 2.5 mph 300 O 112 mph 60 112 mph 300 O 2.1 mph 60" A river flows downstream from West to East at a speed of 5m/s. If Courtney can paddle a boat at 18m/s due North, the speed the boat will be travelling at, to the nearest tenth, will be O 13.0 m/s O 18.7 m/s O 19.1 m/s O 18.2 m/sMarco jogs 6 mph {west) for 45 minutes then turns and jogs 15 mph {South) for 30 minutes. What is the magnitude and bearing of his displacement from his starting point? 8.7 miles [211" ] 8.7 miles [593 ] 16.2 miles [202" ] 16.2 miles [689] To reach their destination, a pilot must fly the plane at at a speed relative to the ground of 210 mph at a bearing of 3453. Knowing that the wind is blowing towards 85 at a speed Of 40 mph, in what direction and at what speed must the pilot point the plane to reach their destination? 2136.8 mph [3543] 206.8 mph [356-] O 213.8 mph [356- ] 220.5 mph [3359] Vector a = 50 mph [E]. What is the magnitude of the vector 1.6a + 4a? O 224 mph O 210 mph O 280 mph O 240 mphA small jet leaves a private airport near San Diego. It travels at 235 mph on a heading of 25 degrees South of East, but is affected by a wind blowing at 60 mph toward 65 degrees West of South. Determine the plane's position after two hours of flight relative to the airport. O 355 miles at 23 degrees North of West 423 miles at 52 degrees North of East 397 miles at 34 degrees North of East O 404 miles at 38 degrees South of East If z = (16, -5) and f = (3, -4), find 2e - 7f. O (53, -33) O (11, 18) O (16, -5) O (13, -1) Without attempting to solve, how many solutions does this system of equations have? 1=2+2 2y = 4x + 4 O An infinite number of solutions O Cannot be determined without solving O One Solution O No Solution