11 3 -21 10. Use properties of determinants to find the value of the determinant 6...
Q4. Find the determinant of the following matrix A by hand. You may use properties of determinants or reduction to reduced row echelon form to minimize the calculations: A= [1 0 12 -1 5 1 - 1 1 1 -1 3 0 0 1
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...
a)Use row reduction and/or cofactor expansion to calculate the
determinant of
c) Calculate the following determinants, using your answer to
part a
det(A^−1 ) det(2A) det(A^2 ) det(A^T A)
3 3 3 -1 2 2 A= 1 9 6 2 2 2 4 2
1. Algebra: Why are all these determinants zero? 3 -1 6 21 1 0 0 0 1 -2 3 -4 1 3 1 2 7 -1 2 2 1 3 5 2 3 4 5 (a) 1 1 1 1 1; (b) 2 5 2; (c) 3 0 1 -73 (d) 3 1 7 11 3 7 3 3 -1 6 21 5 2 6 10 3 3 3 3 2. Algebra: - la b c Given that d e...
Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08 a Find the cofactors C11,C2,C3 of A. b Find the determinant of 1, det(A) [ 2 4 61 Problem 2 Consider the matriz A=008 | 2 5 3 a Use the ero's to put A in upper triangular form 5 Pinul the determinant of A. (A) by keeping track of the row operations in part a and the properties of determinant Problem 3 Consider...
4. Use determinants to find all values of h such that the following linear system has exactly one solution for any b1,b2, bз, ba ER hx4 2x2 3 b2 + hxi 12x4 2хз + hx2 + I1 8x2 - Do not use Maple to calculate any determinants. You are permitted to use the formula for a 3 x 3 determinant Hint: The determinant will be a cubic polynomial in h. You must factor this polynomial. It is a fact h...
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...
5.3.47 Assigned Med Use the determinant theorems to find the value of the determinant 50 -5 5.4 4 =0 15 O -15 50 -5 5 4 4 150 - 15 dures dbook Enter your answer in the answer box and then click Check Answer x All art cho W il F10 d+ х FB F4 FS % 5 & 7 8 9 6 3 4 Y U T E W R к J H G S D F N M...
Full Name 6. a) Use only the Logarithmie Properties to find the exact value of the following expression: log(1) In(e) + 21092() + log (5) log(105) b) Mentally evaluate the following logarithms (exact value): log (16) = log() log(1000) = c) Find the exact value of loge(16). Clearly show the algebraic strategy we developed in class. d) Use the Logarithmic Properties to contract the following logarithmic expression to a single logarithm. Show all your steps and simplify your final answer...
[4 -2 0] 1. Use Gaussian reduction to find the determinant of A = |2 -1 2]. 11 5 7 [4 -2 01 2. Use the permutation expansion to find the determinant of A = 2 -1 2. 11 5 7