S = |----0--()-(0) a) Is S linearly independent? b) Does S span R3? What can you conclude about S? a c) Let vb be an arbitrary vector in R³. Write v as a linear combination of the standard basis vectors C1, C2, C3 for R³. d) Let v = a b be an arbitrary vector in R³. Now write v as a linear combination of C the vectors x, y, z, i.e., find coefficients C1, C2, C3 such that C1x+C2y+C3% = v.
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- The following graph contains four lines (A, B, C and D), each of which has a slope that is either positive, negative, zero, or infinite. Y-axisX-axisBDCA For each of the following scenarios, indicate whether the relationship between the two variables is positive or negative, as well as which line on the previous graph has a slope that reflects this type of relationship. Hint: The X-axis and Y-axis on the graph are not labeled intentionally. You need to substitute the variables from each scenario for the horizontal and vertical axis. For example, in the first scenario, X-axis should be labeled “ ice-cream" and Y-axis should be labeled "The temperature". Scenario Relationship Line As the temperature rises, the demand for ice-cream rises. Negative As the temperature rises, the demand for hot cocoa falls. Positive As the temperature falls, the demand for popsicles falls. Negative True or False: Line B has a slope of infinity.…Refresh your Math & Graphing Skills SOP-A D For each of the following scenarios, indicate whether the relationship between the two variables is positive or negative, as well as which line on the previous graph has a slope that reflects this type of relationship. X-axis Hint: The X-axis and Y-axis on the graph are not labeled intentionally. You need to substitute the variables from each scenario for the horizontal and vertical axis. For example, in the first scenario, X-axis should be labeled The average grade received" and Y-axis should be labeled "The number of hours spent studying". Scenario As the number of hours spent studying rises, the average grade received rises. As the number of hours spent studying falis, the likelihood of getting an A falls. As the number of hours spent watching TV rises, the average grade received falls. True True or False: Line B has a slope of infinity. O False www Relationship Line YU t of estion English (en) Variable Y 24 20 16 12 8 4 O a. y = 8 - 2x. O b. x = 8 + 0.5y. O c. y = 8 + 2x. O d. (3) y = 8 + 0.5x. (1) + + 0 2 4 6 8 10 12 14 16 18 Variable X The linear equation for line (1) on the provided graph is (2)
- 1 1 a) Let A = 1 -1 -1 1 (i) Compute the value of det (A). (ii) For what values of x will the matrix be singular? b) Write down the quadratic form that corresponds to the following matrix. 2 4 2 -1 -3 .4 -3 1Given the functional relationship: y = 14x5/x2 find the value of y when x = 1.5Variable Y 18 A A B 6 6 9 12 15 18 Variable X 15 12 6 3 O 3 لیا Refer to the provided graph. The slope of the line tangent to the curve at point B is
- Erin grows pecans. The number of bushels (B) that she can produce depends on the number of inches of rainfall (R) that her orchards get. The relationship is given algebraically as follows: B = 3,000 + 800R. Match each part of this equation with the correct term. B slope 3,000 dependent variable 800 vertical intercept R independent variableOnly typed answer and please don't use chatgpt otherwise I downvote the answer Assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student teacher ratio by 2 will: A) reduce test scores by 2.28 on average B) result in a test score of 698.9 C) reduce test scores by 2.56 on average D) reduce test scores by 4.56 for every school district PLEASE EXPLAIN WHY C IS CORRECT.Economics
- ) Find and classify the stationary points of the following function: f (x) = 1. [Specify the 1st and 2nd order conditions.] 1. T-15. Suppose a quadratic function is given by y = f(x) = x29x + 8. (a) Does this function represent an upward or downward facing parabola? Explain. Find the x - coordinate of the vertex (or the equation of the vertical line that intersects the parabola at the vertex) of the parabola.(b) Find the roots of the quadratic function. 1 (c) Using information from (a) and (b) draw a well labelled graph of the parabola (in particular, label the vertex and the roots).(d) In the same graph as (c), draw the parabola if it was instead represented by the function f(x) = x2-9x + 21. How many roots does this parabola have?6. Suppose an inverse demand function is given by p =10 - qd and an inverse supply function is given by p = 4+ 2qs. (a) What is the equilibrium price and quantity combination? (b) What happens when the price is above or below the equilibrium price? 7. How many solutions does a system of two equations have? Explain clearly and succinctly.I need answer typing clear urjent no chatgpt used i will give upvotes