Q2) Let M2x2 be the vector space of all 2X2 matrices, and defined T:M2x2 → M2x2 , such that T(A)= A+A" .where A= |a b) Find the Ker (T).

Q: M2,2 is the vector space of all 2 x 2 matrices. List the o element of this vector space.

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Q: solutions of the Inequality r + 6<9?

A: We are given the inequality as : x+6 &lt; 9

Q: Let X = TONT. 1 and 3 0 A = 0 3 1 0 -2 -4 -4 0 3 00 -2 0 0 -4 0 1 -1 01 1 0 0

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Q: (2) Let M₂×2 be the vector space of all 2X2 matrices, and defined T:M 2x2 (A)=A+AT. where A= a [cd]…

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Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: X = 8 8 3 3 ; A = 2 42 0 1 -2 -3 7 3 3 2 9

A: Every matrix of order m×n is represented a linear transformation from Rn→Rm definition of T(x)=Ax

Q: Express the Vector x as a linear combination of the U's U₁ Gl , 02 [1] ·16

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Q: Does the set of all 2x2 matrices form a vector space, please explain.

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Q: Let u be a vector in R" and A be an m × n matrix. If u is orthogonal to each row of A then u is in…

A: Since u is orthogonal to each row of A, it means u is in null space of A.

Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

A: Answer :

Q: Let A= {a1,a2,a3} and B= {b1,b2 b3} be bases for a vector space V, and suppose a, = 5b, - b2, a2 =…

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Q: Q2. Show that M2x2 , the set of all 2× 2 matrices is a vector space. Explain your answer? Good Luck!

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Q: 4 [1] 2. Is the vector 5 in the column space of matrix A = 1 0 -2 −4 4 4 5 3 -13]

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Q: 4. Find representation of the vector v = 2 – 2x+ 6x? with respect to following basis. {1+ 3x + 3x?;…

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Q: Q4 let V=M₂x₂ of the form [a of with standard matrix addition and multiplication form -space-

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Q: find if the vector x is in the range for matrix A

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Q: Notations That Represent A Line

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Q: Let A be an m x n matrix, v be a vector in R", and c be a scalar. Show that A(cv) = c(Av).

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Q: Find a formula for the dimension of the vector space of symmetric n X n matrices.

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A: Given basis of a vector space V:

Q: 3= b, ,b2} and C= (c,.c2} be bases for a vector space V, and suppose b, = - 6c, + 5c2 and b2 = - 4c,…

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Q: Let A and B be m × n matrices. (a) Suppose that v"Aw = v"Bw for all vectors v, w with real entries.…

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