All questions attached. Linear Algebra questions. Work not needed, just need the answers. Most are multiple choice and probably can be found online. Thank you!
1. 2. 3. 4. Student: Sam Henry Date: 06/13/21 Instructor: Course: Assignment: 1.1 Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure. x + 5x1 2 = 9 4x + 7x1 2 = − 3 Find the solution to the system of equations. (Simplify your answer. Type an ordered pair.) Find the point that lies on the line and on the line . See the figure. x ,x1 2 x1 + 2x2 = 4 x1 − x2 = 1 The point that lies on the line and on the line is .x ,x1 2 x1 + 2x2 = 4 x1 − x2 = 1 (Simplify your answer. Type an ordered pair.) Do the three lines , , and have a common point of intersection? Explain. 4x − 8x = 151 2 8x + 40x = − 1381 2 − 4x − 48x = 1531 2 Choose the correct answer below. A. The three lines have at least one common point of intersection. B. The three lines do not have a common point of intersection. C. There is not enough information to determine whether the three lines have a common point of intersection. Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. 1 h 3 5 20 12 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The matrix is the augmented matrix of a consistent linear system if h .= (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. The matrix is the augmented matrix of a consistent linear system if h .≠ (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) C. The matrix is the augmented matrix of a consistent linear system for every value of h. D. The matrix is not the augmented matrix of a consistent linear system for any value of h. x1 x2 5. Find an equation involving g, h, and k that makes this augmented matrix correspond to a consistent system. 1 − 6 6 g 0 7 − 3 h − 2 5 − 9 k What equation must be satisfied for the augmented matrix to correspond to a consistent system? Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer.) A. g h k2 − − = B. g h k2 − + = C. g h k2 + + = D. g h k2 + − = 1. 2. Student: Sam Henry Date: 06/13/21 Instructor: Course: Assignment: 1.2 Row reduce the matrix to reduced echelon form. Identify the pivot positions in the final matrix and in the original matrix, and list the pivot columns. 1 2 3 4 3 4 5 6 5 6 7 8 Row reduce the matrix to reduced echelon form and identify the pivot positions in the final matrix. The pivot positions are indicated by bold values. Choose the correct answer below. A. 1 2 0 0 0 0 1 3 0 0 0 0 B. 1 0 − 1 − 2 0 1 2 3 0 0 0 0 C. 1 0 0 0 0 1 0 0 0 0 1 1 D. 1 0 0 1 0 1 0 3 0 0 1 5 Identify the pivot positions in the original matrix. The pivot positions are indicated by bold values. Choose the correct answer below. A. 1 2 3 4 3 4 5 6 5 6 7 8 B. 1 2 3 4 3 4 5 6 5 6 7 8 C. 1 2 3 4 3 4 5 6 5 6 7 8 D. 1 2 3 4 3 4 5 6 5 6 7 8 List the pivot columns. Select all that apply. A. Column 1 B. Column 4 C. Column 2 D. Column 3 Find the general solution of the system whose augmented matrix is given below. 2 − 5 9 0 4 − 10 18 0 6 − 15 27 0 Choose the correct answer below. A. x1 = 5 2 x2 − 9 2 x3 x2 is free x3 is free B. x1 = − 2x2 x2 = 5x3 x3 is free C. x1 = 2 x2 = − 5 x3 = 9 D. The system has no solutions. 3. Choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. hx1 + x2 = 4 4x1 + 8x2 = k a. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.) A. The system has no solutions only when k and h is any real number.≠ B. The system has no solutions only when k and h is any real number.= C. The system has no solutions only when h and k is any real number.≠ D. The system has no solutions only when h and k is any real number.= E. The system has no solutions only when h and k .= ≠ F. The system has no solutions only when h and k .≠ ≠ G. The system has no solutions only when h and k .= = H. The system has no solutions only when h and k .≠ = b. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.) A. The system has a unique solution only when h and k is any real number.= B. The system has a unique solution only when h and k .= ≠ C. The system has a unique solution only when h and k .≠ ≠ D. The system has a unique solution only when k and h is any real number.= E. The system has a unique solution only when h and k is any real number.≠ F. The system has a unique solution only when h and k .= = G. The system has a unique solution only when k and h is any real number.≠ H. The system has a unique solution only when h and k .≠ = c. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.) A. The system has many solutions only when h and k .= ≠ B. The system has many solutions only when h and k .≠ = C. The system has many solutions only when h and k .= = D. The system has many solutions only when h and k .≠ ≠ E. The system has many solutions only when h and k is any real number.≠ F. The system has many solutions only when k and h is any real number.≠ G. The system has many solutions only when h and k is any real number.= H. The system has many solutions only when k and h is any real number.= 4. Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial for the data ( , ), ( , ), ( , ). That is, find , , and such that the following is true. p(t) = a + a t + a t0 1 2 2 1 11 2 19 3 23 a0 a1 a2 a0 + a (1)1 + a (1)2 2 = 11 a0 + a (2)1 + a (2)2 2 = 19 a0 + a (3)1 + a (3)2 2 = 23 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The interpolating polynomial is p(t) .= B. There are infinitely many possible interpolating polynomials. C. There does not exist an interpolating polynomial for the given data. 1. 2. 3. Student: Sam Henry Date: 06/13/21 Instructor: Course: Assignment: 1.3 Compute and .u + v u − 3v , u = − 1 5 v = − 6 1 (Simplify your answer.)u + v = (Simplify your answer.)u − 3v = Write a system of equations that is equivalent to the given vector equation. x1 x2 3 − 4 6 + 3 0 − 7 = 2 − 3 7 Choose the correct answer below. A. 3x1 + 3x2 = 2 − 4x1 + x2 = − 3 6x1 − 7x2 = 7 B. 3x1 + 3x2 = 2 − 4x1 = − 3 6x1 − 7x2 = 7 C. 3x1 + 3x2 = − 3 − 4x1 = 2 6x1 − 7x2 = 7 D. 3x1 + 3x2 = 7 − 4x1 = − 3 6x1 − 7x2 = 2 Determine if b is a linear combination of a1 , a2 , and a3. a1 , a2 , a3 , b= 1 − 3 0 = 0 1 2 = 6 − 6 24 = 4 − 3 18 Choose the correct answer below. A. Vector b is not a linear combination of a1 , a2 , and a3. B. Vector b is a linear combination of a1 , a2 , and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the fourth column. C. Vector b is a linear combination of a1 , a2 , and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column. D. Vector b is a linear combination