To identify: The system of equations by finding the reduced row echelon form for the augmented matrix.
The value of
Given information:
The given equation is.
Explanation:
Consider the given information.
To obtain the augmented matrix of a system, write out the coefficients as entries, aligning those with the same variables, and placing 0 for variables that are not present. The last column corresponds to the constants.
So, its corresponding augmented matrix is:
Apply elementary row operation to obtain a reduced row echelon from of the matrix.
This corresponds to the system of equation.
Since
So, the value of
Chapter 7 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
- 1. Determine whether the following sets are subspaces of $\mathbb{R}^3$ under the operations of addition and scalar multiplication defined on $\mathbb{R}^3$. Justify your answers.(a) $W_1=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=3 a_2\right.$ and $\left.a_3=\mid a_2\right\}$(b) $W_2=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=a_3+2\right\}$(c) $W_3=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 2 a_1-7 a_2+a_3=0\right\}$(d) $W_4=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1-4 a_2-a_3=0\right\}$(e) $W_s=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1+2 a_2-3 a_3=1\right\}$(f) $W_6=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 5 a_1^2-3 a_2^2+6 a_3^2=0\right\}$arrow_forward3 Evaluate the double integral 10 y√x dy dx. First sketch the area of the integral involved, then carry out the integral in both ways, first over x and next over y, and vice versa.arrow_forwardQuestion 2. i. Suppose that the random variable X takes two possible values 1 and -1, and P(X = 1) = P(X-1)=1/2. Let Y=-X. Are X and Y the same random variable? Do X and Y have the same distribution? Explain your answer. ii. Suppose that the random variable X~N(0, 1), let Y=-X. Are X and Y the same random variable? Do X and Y have the same distribution? Explain your answer.arrow_forward
- Problem 4. Let f(x, y) = { Find P(X <1/2|Y = 1/2). c(x + y²) 0arrow_forwardQize f(x) x + 2x2 - 2 x² + 4x² - 4 Solve the equation using Newton Raphsonarrow_forwardSolve please thanks!arrow_forwardSolve please and thank youarrow_forwardAccording to Newton's law of universal gravitation, the force F between two bodies of constant mass GmM m and M is given by the formula F = , where G is the gravitational constant and d is the d² distance between the bodies. a. Suppose that G, m, and M are constants. Find the rate of change of force F with respect to distance d. F' (d) 2GmM b. Find the rate of change of force F with gravitational constant G = 6.67 × 10-¹¹ Nm²/kg², on two bodies 5 meters apart, each with a mass of 250 kilograms. Answer in scientific notation, rounding to 2 decimal places. -6.67x10 N/m syntax incomplete.arrow_forwardSolve please and thank youarrow_forwardmv2 The centripetal force of an object of mass m is given by F (r) = rotation and r is the distance from the center of rotation. ' where v is the speed of r a. Find the rate of change of centripetal force with respect to the distance from the center of rotation. F(r) b. Find the rate of change of centripetal force of an object with mass 500 kilograms, velocity of 13.86 m/s, and a distance from the center of rotation of 300 meters. Round to 2 decimal places. N/m (or kg/s²) F' (300)arrow_forwardSolve work shown please and thanks!arrow_forwardGiven the following graph of the function y = f(x) and n = = 6, answer the following questions about the area under the curve from x graph to enlarge it.) 1 (Round your answer to within two decimal places if necessary, but do not round until your final computation.) a. Use the Trapezoidal Rule to estimate the area. Estimate: T6 G b. Use Simpson's Rule to estimate the area. Estimate: S6 - ID = 0 to x = 6. (Click on aarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





