Evaluate the determinants in Problems 1 to 6 by the methods shown in Example 4. Re-member that the reason for doing this is not just to get the answer (your computer cangive you that) but to learn how to manipulate determinants correctly. Check your answersby computer.-251731.3 4-22.24-35 6-3112111.1-24248.2-93.4.13610-46.8.414.1020-93lo 1|10 1 1|1 1 0 1|1 1 1 0 1|1 1 1 1 0|7-3511.127-11.4.15.-3-16.18.6.-2-741-57 5

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Answered: Evaluate the determinants in Problems 1…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter11: Matrices And Determinants

Section11.CR: Chapter Review

Problem 11CC

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23.The following problem illustrates a danger that occurs because of round-off error when nearly equal numbers are subtracted and the difference is then multiplied by a large number. Evaluate the quantity 1000⋅∣∣∣6.01018.042.0046.000∣∣∣1000·6.01018.0402.00416.000 in the following ways: a.First round each entry in the determinant to two digits.
2. If the determinant of a 5×5 matrix A is det(A)=6, and the matrix C is obtained from A by swapping the second and third rows, then what is det(C)? 3. If the determinant of a 4×4 matrix A is det(A)=8, and the matrix D is obtained from A by adding 2 times the fourth row to the first, then what is det(D)?
1. If the determinant of a 5×5 matrix A is det(A)=9, and the matrix B is obtained from A by multiplying the first row by 8, then what is det(B)? 2. If the determinant of a 5×5 matrix A is det(A)=6, and the matrix C is obtained from A by swapping the second and third rows, then what is det(C)? 3. If the determinant of a 4×4 matrix A is det(A)=8, and the matrix D is obtained from A by adding 2 times the fourth row to the first, then what is det(D)? 4. If A and B are 2×2= matrices, det(A)=5, det(B)=4, theni. det(AB)= ii. det(−3A)= iii. det(A^T)= iv. det(B^−1)= v. det(B^2)=
40 - Which of the following is the definition of the determinant of the coefficients of the system of linear equations of order n. a) It is the determinant created by placing the constants on the right side of the system instead of the second column elements in the coefficients determinant. B) It is the determinant formed from the coefficients of the unknowns. NS) It is the determinant created by placing the constants on the right side of the system instead of the fifth column elements in the coefficients determinant. D) It is the determinant created by placing the constants on the right side of the system instead of the first column elements in the coefficients determinant. TO) It is the determinant created by placing the constants on the right side of the system instead of the last column elements in the coefficients determinant.
Show that the elimination method of computing the value of the determinant of an n × n matrix involves [n(n − 1)(2n − 1)]/6 additions and [(n − 1)(n2 + n + 3)]/3 multiplications and divisions. Hint: At the ith step of the reduction process, it takes n − i divisions to calculate the multiples of the ith row that are to be subtracted from the remaining rows below the pivot. We must then calculate new values for the (n − i)2 entries in rows i + 1 through n and columns i + 1 through n.
Problem 1: Consider the following two square matrices A=[2345], B=[5−32−6] Find A + B and A-2B Find the products AB and BA. Is AB = BA, why or why not? Is A a singular matrix, why or why not? Problem 2: Find the determinant of A, that is |A|, if A=⎡⎢⎣230−15−3042⎤⎥⎦Problem 3: Find the determinant of AT, that is |AT|, using Matrix A defined in problem 2 aboveProblem 4: Find the inverse of a 2 X 2 matrix B defined in problem 1 above
A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard devia- tion of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L. *8.31 What are the appropriate null and alternative hypoth- eses to compare the means of the two groups?*8.32 What is the appropriate test procedure for the hy- potheses in Problem 8.31? How can we find p value? dont use excel. solve the step by step
A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard devia- tion of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L.*8.32 What is the appropriate test procedure for the hy- potheses ? Find the p value using the F test. Solve the step by step. do nut use excell
A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard devia- tion of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L.*8.32 What is the appropriate test procedure for the hy- potheses ? Find the p value using the F test. Solve the step by step. do not use excell. JUST I WANT TO LEARN P VALUE Using the F Test . BE CAREFUL !!!!!
If the determinant of a 5×5 matrix A is det(A)=8, and the matrix C is obtained from A by swapping the third and fourth rows, thendet(?)=
A possible important environmental determinant of lungfunction in children is the amount of cigarette smoking in thehome. Suppose this question is studied by selecting twogroups: Group 1 consists of 23 nonsmoking children 5−9years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard devia-tion of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who havea mean FEV of 2.3 L and a standard deviation of 0.4 L. *8.31 What are the appropriate null and alternative hypoth-eses to compare the means of the two groups? *8.32 What is the appropriate test procedure for the hy-potheses in Problem 8.31? *8.33 Carry out the test in Problem 8.32 using the critical-value method. *8.34 Provide a 95% CI for the true mean difference in FEVbetween 5- to 9-year-old children whose parents smoke andcomparable children whose parents do not smoke.*8.35 Assuming this is regarded as a pilot study, how many…
Suppose A is a 5 by 5 matrix. Its entries in row 1 multiply determinants (cofactors) in rows 2-5 to give the determinant. Can you guess a "Jacobi formula" for det A using 2 by 2 determinants from rows 1-2 times 3 by 3 determinants from rows 3-5? Test your formula on the -1, 2, -1 tridiagonal matrix that has determinant= 6.

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