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solve and please write explanation as well. 2. Consider the following matrices: [1 2 1-1 3...
Problem 4 (12 points, 2 for each part) In each of the following parts, as- sume that the matrices A, B, C have sizes that make the sums, differences, and products in that part well-defined. Say whether the statement is always true (i.e., true for all matrices of appropriate sizes), sometimes but not al- ways true, or always false. (You may abbreviate answers as T, S, and F, respectively, but make sure your handwriting is unambiguous.) (a) AB = BA...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
answer the following in details.. Q2. Two matrices can be multiplied in number of different ways. Below is given four different ways of multiplying two matrices: 1) Using MATLAB generate any two matrices (A1oxs and Bsx10) and compute AB using all four 2) 3) methods Which of these methods would be computationally less expensive? Can you suggest any other way of multiplying these two matrices? Q2. Two matrices can be multiplied in number of different ways. Below is given four...
1. Consider the following matrices. A= 1 2 -1 0 3 4 B 2 3-4 5 1 and C= -[-1:] Compute each of the following, if it is defined. If an expression is undefined, explain why. (a) (4 points) A+B (b) (4 points) 2B (c) (4 points) AC (d) (4 points) CB
2. Partitioned matrices A matrix A is a (2 x 2) block matrix if it is represented in the form [ A 1 A2 1 A = | A3 A4 where each of the A; are matrices. Note that the matrix A need not be a square matrix; for instance, A might be (7 x 12) with Aj being (3 x 5), A2 being (3 x 7), A3 being (4 x 5), and A4 being (4 x 7). We can...
Exercise 1 Consider the two matrices o 3 1 0 ) Say whether the following matrix elements are defined, and if so, give their value: 13, 1M31,M22, V13, V31, /V22 (i) Write MIT and [NI in matrix array notation. (iii) Say whether the following matrices are defined (and explain why). If they are defined, compute them and write the result in matrix array notation
Consider the following matrices: 1 2 A= 3-4 2 3 B= 3 2 1 1 0 2 C= 2 1 3 -1 1 1 1 4 5 -4 2 5 1 3 4 1 0 1 1 - 2 D= E= F 4 1 31 7 3 2 Find each of the following, if possible. If it is not possible, explain your reasoning. 1 (a) AB (9) BAT (b) BA (h) (A + B) E (C) CD + E ()...
Matrix Methods/Linear Algebra: Please show all work and justify the answer! 1. Consider the following matrices. [-1:] 1 2 2 0 A= -10.B=3-4 and C= 3 4 5 Compute each of the following, if it is defined. If an expression is undefined, explain why. (a) (4 points) A+B (b) (4 points) 2B (e) (4 points) AC (d) (4 points) CB
Need help!! 1) Let A, B, C, and D be the matrices defined below. Compute the matrix expressions when they are defined; if an expression is undefined, explain why. [2 0-1] [7 -5 A= .B -5 -4 1 C- ,D= (-5 3] [I -3 a) AB b) CD c) DB d) 3C-D e) A+ 2B 2) Let A and B be the matrices defined below. 4 -2 3) A=-3 0, B= 3 5 a) Compute AB using the definition of...
(4) The Pauli spin matrices are a set of 3 complex 2 x 2 matrices that are used in quantum mechanics to take into account the interaction of the spin of a particle with an external electromagnetic field. σ2 10), (a) Find the eigenvalues and corresponding eigenvectors for all three Pauli spin matrices. Show all of vour work (b) In Linear Algebra, two matrices A and B are said to commute if AB BA and their commutator defined as [A,...