Find the linear combination 3s1 + 4s2 + 5s3 = b. Then write bas a matrix vector multiplication Sx, with 3, 4, 5 in x. Compute the three dot products (row of S) • x: s1 = [ 1/1/1]  s2= [ 0/1/1] ] s3= [ 0/0/1 ]  go into the columns of s.

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Q: Is this the correct definition of upper triangular, for a matrix A? Aij * 0 when j 2 i O Yes No

A: Since you have asked multiple questions , we will solve first question for you. If you want any…

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Q: the matrIX A into a product QDQ" where Q is orthogonal and D is diagonal.

A: Given,          A=-5-1-1-1-3-1-1-1-3

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A: The solution is given as

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A: Given that the matrices are equal. x4=6y

Q: 4. Find the standard matrix for T where Ta2) =(2x,+x -2,).

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A: Given       A=116-1291-23

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Q: Let a Consicler the matrix 4. A= S23 87.3. Find Mz, C1z and Mzz, Czz

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Q: Find all pairs (x,y) for which matrix B is not invertible, where 1 1 B = 2 1 1 0 -1 y

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A: Given : f1(x, y) = 5x+6y f2(x, y) = 5x²-4y² To find : Determinant of jacobian matrix

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Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

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Q: Consider the ordered bases B = {1+x, 1 – x} and B' = {u1, U2} for P1(IR), and suppose that 2 Q = ( -…

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Q: 2rị + 13 T: R' → R?, T 21, 22, 13, L4 ER -12 - 3r4

A: Given  and the standard bases are given by

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A: Given that, B'=8, 11, 0, 7, 0, 10, 1, 4, 6 and x=5, 34, -2

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A: M = 0 will be the right answer.

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Q: Express the quadratic form as v Av, where A is a symmetric matrix. x² + 3y² + 5z² - 4xy+3yz + 10xz

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Q: O Find the transforma tion matrix that wotates the axis X of a rec tangu lar coor dinale system 60…

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Q: Suppose that a 3 x 3 matrix A factors into a product: 1 0 0111 U12 U13] A = 121 1 0 0 U22 U23 Ll31…

A: Given that  A = 100l2110l31l321 u11u12u130u22u2300u33 We have to determine the value of  det A.