5. Use determinants to indicate whether or not the following systems have unique solutions. (a) (2...
ECS423U (2019) Page 3 Question 2 (Determinants and Vector Spaces) a) Consider the following system of linear equations: kx + y +z= 1 I + y + 1 x + y + 1 Use determinants to find those values of k for which the system has: 1) A unique solution 24 iv) More than one solution v) No solution HINT. solving the determinant equation, please use a trick: just add and substract [15 marks] b) Consider the following matrix: 1...
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Problem 1. Solve the following systems of linear equations: 4x+3y + z = 9 3x+y-z = 3 x4 Problem 2. Find the values of the parameters a and p for which the system x+5y = 6, has: (i) a unique solution, (ii) infinitely many solutions, (iii) no solutions. Hint: Use the following fact: a system with as many unknowns as equations...
A linear system may have a unique solution, no solution, or infinitely many solutions. Indicate the type of the system for th following examples by U , N , or I7x+3y= pi 4x-6y= pi^2 2x+3y= 0 4x+6y= 0 2x+3y=1 4x+ 6y= 1x+y=5 x+2y=102x-3y=5 4x-6y=10
7. This question involves the concept of determinants and partitioned matrices. Historically, determinants first arose in the context of solving systems of linear equations for one set of variables in terms of another. For example, if the coefficient matrix of the system u= ax + by v=cx + dy is invertible, then the equations can be solved for x and y in terms of u and v as au – cu 2= du - bv ad - bc y =...
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2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coumn expansions or elementary row operations and the properties of determinants). Are A and B invertible? Calculate their inverses if they exist 1b. Are the columns of A linearly dependent or linearly independent? Find the dimension of Nul A and the rank of A. What can you say about the number of...
Review Uuristas A red blood cell is placed into each of the following solutions. Indicate whether crenation, hemolysis, or neither will occur. • Solution A: 2.19 % (m/v) NaCl • Solution B: 4.42 % (m/v) glucose • Solution C: distilled H2O • Solution D: 9.6 % (m/v) glucose • Solution E: 5.0% (m/v) glucose and 0.9% (m/v) NaCl Drag each solution to the appropriate bin. View Available Hints) 0000 DE Crenation
Question 4 (21 pts.) Assuming the A-systems in the following structures are flat, indicate whether they are aromatic, anti-aromatic or non-aromatic. H
EXERCISE 5.2 1. Evaluate the following determinants: 2. Determine the signs to be attached to the relevant minors in order to get the following cofactors of a determinant: (C13l, IC23i, (C3sl. Canl, and Cu). 6. Find the minors and cofactors of the third row, given EXERCISE 5.3 4. Test whether the following matrices are nonsingular: EXERCISE 5.4 4. Find the inverse of each of the following matrices: 6. Solve the system Ax=d by matrix inversion, where EXERCISE 5.5 1. Use Cramer's rule to solve the following equation systems: 3. Use Cramer's...
Question 4 (21 pts.) Assuming the s-systems in the following structures are flat, indicate whether they are aromatic, anti-aromatic or non-aromatic.
2. Indicate whether each of the following solutions will exhibit a positive deviation from Raoult's law, a negative deviation or no deviation. Explain briefly. H : CI-C-CI: and C CH3 CH3 : CI: 11 a. CH,OCH3 and CH3CH2OH