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Concept explainers
In Exercises 43–48, use matrix inversion to solve the given systems of linear equations. (You solved similar systems using row reduction in Chapter 4.) [HinT: See Quick Example 6.]
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Chapter 4 Solutions
Bundle: Finite Mathematics, Loose-leaf Version, 7th + WebAssign Printed Access Card for Waner/Costenoble's Finite Mathematics, 7th Edition, Single-Term
- In Exercises 7–10, the augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate row operations and describe the solution set of the original system. 1 7 3 -4 1 -4 1 -1 3 7. 8. 1 7 1 1 -2 0 -4 0 -7 1 -1 1 -3 9. 1 -3 -1 4arrow_forwardIn Exercises 1–4, determine if the system has a nontrivial solution. Try to use as few row operations as possible.arrow_forwardIn Exercises 19–20, solve the matrix equation for X. 1 -1 1 -1 5 7 8. 19. 2 3 0| X = 4 -3 1 1 3 5 -7 2 1 -arrow_forward
- Write down the (1,2) minor of the matrix 1 -1 3 > -1 1 0 1 4 5arrow_forwardPlease solve this linear algebra question involving ranking of properties in matrix System. I want to verify to see if I have good answer. Pls ASAP, thank youarrow_forwardSolve the following linear equations using the 5 methods: (Gaussian Elimination, Gauss-Jordan Elimination, LU Factorization, Inverse Matrix and Cramer's Rule). Show your complete solutions. b. 2x1 — 6х, — Хз 3D — 38 -3x1 – x2 + 7x3 = -34 -8x1 + x2 – 2x3 = -20arrow_forward
- Convert the augmented matrix [5 -3 4 2 || || -3 0 -5 to the equivalent linear system. Use x1, x2, and x3 to enter the variables x₁, x2, and x3. 8:8arrow_forward2. Solve for x in the given matrix equalitiesarrow_forward2 5 31 5. Write X =|-3 6 0 as the sum of a skew symmetric and a symmetric 4 1 1] matrix.arrow_forward
- Consider the following linear system: x2 + 2x3 + x4 -1, -x1 + x2 – x3 – 2x4 2.x1 + x2 + 8x3+ 7x4 -4x1 + 3x2 – 6x3 – 9x4 -3, 3, -11, in variables x1, x2, x3, and x4. Hint: You only have to row reduce one augmented matrix to answer all of the questions below. A. What is the reduced row echelon form of the augmented matrix? B. What is the rank of the matrix? C. Of the variables x1, x2, 3, and x4, which are free (i.e. independent) and which are dependent? D. Write the general solution in parametric form. E. Let A be the coefficient matrix of the system. Is A invertible? F. What is the determinant of A? G. What is Nul(A)? H. Express Nul(A) in the form Span({T1,... , ix}).arrow_forwardLet matrix B = 5-21 what is The 14-2 3 - 12 2. reduced Yow echelon form of B.arrow_forward-1 Find the rank of the matrix 2 4 -2 3 -7 3.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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