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Rule of Sarrus for the determinant of 3 x 3-matrices. Let a11 a12 a13 A=|a21 a22 a23 a3i a32 a33 ...
Let 1) a11 x1 + a12 x2 + a13 x3 = b1 2) a21 x1 +...
Let 1) a11 x1 + a12 x2 + a13 x3 = b1 2) a21 x1 + a22 x 2+ a23 x3 = b2 3) a31 x1 + a32 x 2+ a33 x 3 = b3 SHOW that if det(A) does not equal 0, where det (A) is the determinant of the coefficient matrix, then x2= det(A2)/det(A) where det (A2) is the determinant obtained by replacing the second column of det (A) by (b1, b2, b3) to the power T.
A matrix A has 3 rows and 4 columns: a11 a12 a13 a14 a21 a22...
A matrix A has 3 rows and 4 columns: a11 a12 a13 a14 a21 a22 a23 a24 a31 a32 a33 a34 The 12 entries in the matrix are to be stored in row major form in locations 7609 to 7620 in a computer’s memory. This means that the entires in the first row (reading left to right) are stored first, then entries in the second row, and finally entries in the third row. Which location with a22 be stored...
please show steps Let 0 a12 a13 a14 0 a34 a42 023 a43 0 a14 a31 a24 a41 0 a12 a32 a13 a21 0 a21 0 a2 a2 a31 a32 0 a34 b...
please show steps
Let 0 a12 a13 a14 0 a34 a42 023 a43 0 a14 a31 a24 a41 0 a12 a32 a13 a21 0 a21 0 a2 a2 a31 a32 0 a34 be two antisymmetric matrices, where ak -aki, or ATA and BT -B. Show that AB BA and present this diagonal matrix as follows BA AB (a32014 +a13024 a21a34) I, where I is the 4 x 4-identity matrix. Find A-1 and B-1. (H. Minkowski, 1908)
Let 0 a12 a13...
Given the matrix A below, answer the following questions: A _ | a11 a12 a21 a22...
Given the matrix A below, answer the following questions: A _ | a11 a12 a21 a22 O 4A 8A O 16A O Cannot add two matrices of the same dimension b)A 2a11 2 a12-21 La21-2 a22 2 O True O False C)A-11 O True O False d) (AT)-? O A O 1 O A-1 e) (AT)T = A O True O False
QUESTION 3 Player 2 D A a11, b11 a12, b12 Player 1 a21, b21 a22, b22...
QUESTION 3 Player 2 D A a11, b11 a12, b12 Player 1 a21, b21 a22, b22 аз1, bз1 аз2, bз2 Consider the game in normal form in the picture above. For strategy A to be the (strict) dominant strategy it is sufficient that a. a11 > a21 and a12 > a22 · D.a11 > a21 and a11 > a31 · C. None of the other answers apply. a11 > b11 and a12 > b11 .
A3.2 Let L1 and L2 be two lnes in R3 given by Suppose that Li and...
A3.2 Let L1 and L2 be two lnes in R3 given by Suppose that Li and L2 meet at a unique point. Find all pos- sible reduced row echelon forms that the matrix a11 a12 13 a21 a22 a23 a31 a32 a33 a1 a42 a43 b can be reduced to vi a elementary row operations. You mus ustify vour answer
linear algebra Let V (71, 72, 3}, where 71 73=(2,0,3). (1,3,-1), 2 = (0, 1,4), and...
linear algebra
Let V (71, 72, 3}, where 71 73=(2,0,3). (1,3,-1), 2 = (0, 1,4), and (a) Prove: V is a basis. (b) Find the coordinates of (b, b2, bs) with respect to V = {71, U2, 3,}. (c) Suppose M and M' are matrices whose columns span the same vector space V. Let b be the coordinates of relative to M. Write a matrix equation that gives b', the coordinates of relative to M'. (Your answer should be a...
a12 an a2n a21 a22 Problem 2. Given an n x n matrix A = we define the trace of A, denoted : апn an2 anl tr(A), by n tr(...
a12 an a2n a21 a22 Problem 2. Given an n x n matrix A = we define the trace of A, denoted : апn an2 anl tr(A), by n tr(A) = aii a11 +:::+ann- i=1 (a) Prove that, for every n x m matrix A and for every m x n matrix B, it is the case that tr(AB) 3D tr(ВА). tr(A subspace V C R". Prove that norm (b) Let (c) Let P be the matrix of an orthogonal...
ANSWER SHOULD BE NEAT CLEAN AND WELL EXPLAINED.HANDWRITTEN NEAT CLEAN,EACH STEP SHOULD BE EXPLAINED WELL Find...
ANSWER SHOULD BE NEAT CLEAN AND WELL EXPLAINED.HANDWRITTEN NEAT
CLEAN,EACH STEP SHOULD BE EXPLAINED WELL
Find the M to meet the Lyapunov equation in (3.59) with What are the eigenvalues of the Lyapunov equation? Is the Lyapunov equation singular? Is the solution unique? Repeat Problem 3.31 for B- Ci- A1 -2 with two different C 3.7 Lyapunov Equation Consider the equation AM +MB C (3.59) where A and B are, respectively, n x n andmx m constant matrices. In order...
Please answer this using matrices quick thanks 1. Let A be a 3 x 3 matrix...
Please answer this using matrices quick thanks
1. Let A be a 3 x 3 matrix with det (A) 4, and suppose the matrix B is obtained from A by performing the following elementary row/column operations to A: -a Ra+ Rs For what value(s) of a does det(B)-6?
please show steps
Let 0 a12 a13 a14 0 a34 a42 023 a43 0 a14 a31 a24 a41 0 a12 a32 a13 a21 0 a21 0 a2 a2 a31 a32 0 a34 be two antisymmetric matrices, where ak -aki, or ATA and BT -B. Show that AB BA and present this diagonal matrix as follows BA AB (a32014 +a13024 a21a34) I, where I is the 4 x 4-identity matrix. Find A-1 and B-1. (H. Minkowski, 1908)
Let 0 a12 a13...
Given the matrix A below, answer the following questions: A _ | a11 a12 a21 a22 O 4A 8A O 16A O Cannot add two matrices of the same dimension b)A 2a11 2 a12-21 La21-2 a22 2 O True O False C)A-11 O True O False d) (AT)-? O A O 1 O A-1 e) (AT)T = A O True O False
QUESTION 3 Player 2 D A a11, b11 a12, b12 Player 1 a21, b21 a22, b22 аз1, bз1 аз2, bз2 Consider the game in normal form in the picture above. For strategy A to be the (strict) dominant strategy it is sufficient that a. a11 > a21 and a12 > a22 · D.a11 > a21 and a11 > a31 · C. None of the other answers apply. a11 > b11 and a12 > b11 .
A3.2 Let L1 and L2 be two lnes in R3 given by Suppose that Li and L2 meet at a unique point. Find all pos- sible reduced row echelon forms that the matrix a11 a12 13 a21 a22 a23 a31 a32 a33 a1 a42 a43 b can be reduced to vi a elementary row operations. You mus ustify vour answer
linear algebra
Let V (71, 72, 3}, where 71 73=(2,0,3). (1,3,-1), 2 = (0, 1,4), and (a) Prove: V is a basis. (b) Find the coordinates of (b, b2, bs) with respect to V = {71, U2, 3,}. (c) Suppose M and M' are matrices whose columns span the same vector space V. Let b be the coordinates of relative to M. Write a matrix equation that gives b', the coordinates of relative to M'. (Your answer should be a...
a12 an a2n a21 a22 Problem 2. Given an n x n matrix A = we define the trace of A, denoted : апn an2 anl tr(A), by n tr(A) = aii a11 +:::+ann- i=1 (a) Prove that, for every n x m matrix A and for every m x n matrix B, it is the case that tr(AB) 3D tr(ВА). tr(A subspace V C R". Prove that norm (b) Let (c) Let P be the matrix of an orthogonal...
ANSWER SHOULD BE NEAT CLEAN AND WELL EXPLAINED.HANDWRITTEN NEAT
CLEAN,EACH STEP SHOULD BE EXPLAINED WELL
Find the M to meet the Lyapunov equation in (3.59) with What are the eigenvalues of the Lyapunov equation? Is the Lyapunov equation singular? Is the solution unique? Repeat Problem 3.31 for B- Ci- A1 -2 with two different C 3.7 Lyapunov Equation Consider the equation AM +MB C (3.59) where A and B are, respectively, n x n andmx m constant matrices. In order...
Please answer this using matrices quick thanks
1. Let A be a 3 x 3 matrix with det (A) 4, and suppose the matrix B is obtained from A by performing the following elementary row/column operations to A: -a Ra+ Rs For what value(s) of a does det(B)-6?
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