In Problems 1–6 write the given linear system in matrix form.
4.
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- 7. Invert the following matrix 3x – 2y = 9 -x + 3y = 3 |arrow_forward31 32 = 1 + 3x2 1 + 2x3 + 324 Y3 3x2 + x3 Write the matrix A such that y = Ax |arrow_forwardProblem 13. Write the matrix M = where Then z = (a) 1 (b) 2 (c) 3 (d) 4 A 13 24 as a linear combination of the form M = A + B + zC, 8 B= ---- and C=arrow_forward
- Suppose that 2 3 Solve the linear system Ax = b for each of the following matrices b: 8 (b) 15 (a)arrow_forward2) A researcher theorizes that there is a linear relationship between the number of pets a person owns and their square footage of living space (measured in 1000 of square feet). Answer the questions below with the following data: (1.2,2), (1.1,1), (0.9,3), (1.5,3), (1.45,2), (1.1,2) Set up the matrix that are required to do the calculations: a. b. Calculate b C. Calculate r, R² and what does this tell us? d. Given the ANOVA table, with the test the fit of the model? (note a = 0.05) Source Df SS MS Model 2 28.1987 14.0994 Residual 4 2.8013 0.7003 Total 6 31 Build a 95% confidence interval for b₁ e.arrow_forwardProblem 5. Let A be an n x n real symmetric matrix that satisfies A³ = -A. Show that A must be the zero matrix.arrow_forward
- 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z? – 2xy – 2xz – 2yz, and classify it.arrow_forwardProblem 1. --B7--88. [28]. U= = Determine whether the matrix v = [41 lies in span{u, w}, wherearrow_forward1.2. Find a matrix A for which a1,1 = a2,2 = a3,3 = 1, but elimination (with no row exchanges) produces two negative pivots (the first pivot is 1).arrow_forward
- 6. Give an example of two matrices, A and B, neither of which contains any zero entries whose product AB = 0, the zero matrix.arrow_forward0.4 0.06 Let A be the technology matrix A = where Sector 1 is paper and Sector 2 is wood. Fill in the missing quantities. 0.6 0.02 (a) x units of wood are needed to produce one unit of paper. X units of paper are used in the production of one unit of paper. (b) (c) The production of each unit of wood requires the use of x units of paper. Enter a number.arrow_forward1. Suppose that we have a n × 10 matrix (n rows and 10 columns) where the entries are either 0 or 2. What is the smallest value of n which guarantees that the matrix will have two identical rows? Justify your answer.arrow_forward
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