Let R= [0, a, b, ct + a 6 ( a 6 2 a O 2 G G b C 0 a & Sola ه حب a 0 a b ( a b ( States all Subrings of R States all ideal of R ? b O ( a b (

Q: Let W = {(x, y) E R² : x, y > 0}. Define addition + of any two elements (x, y), (w, z) E W by (х, у)…

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Q: N 3 -1l Find the adjoint of A: A =| 1 6 3.Then verify that A (adj A)= (det A)I. 2 -4 0

A: Verification:Compute adj(A) as follows.

Q: Let a, b, q, r E Z and assume that a and b are not both zero and b and r are not both zero. Show…

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Q: Ex: tet R = {o, a,b,c} a G O a b ( وه هه 2 2 G 6 ( 0 a C b a O a b a b 2/2 ( в с @ Show that (B,…

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Q: nd a, b e R such that 4 5 a + bi 1- 2i i - 2 i- 2

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Q: Let and 001 1 0 0 2 1 A = 0 If the entries of A and v belong to Z3, what is the third entry of Av? 2…

A: Recall matrix multiplication and modulo arithmetic.

Q: 112х+ 7 G Зx+ 16 E

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Q: Which ones are echelon form, reduced echelon form or not echelon form?

A: To find which of the matrices are in echelon form, reduced echelon form or not in echelon form.

Q: Let W = {(x, y) E R² : x, y > 0}. Define addition + of any two elements (x, y), (w, z) E W by (x, y)…

A: Let u=(x,y) and v=w,z be any two elements of W, where w,x,y,z>0. Use the definition of addition…

Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

A: See the attachment

Q: 6. show that the set A = {P= (₁4₁2) (R³ | 1²4 + √²2+x2 is an open out.

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Q: Show that I+J is an ideal of L where I+J ={x+y:x∈I, y∈J}.

A: Given that and  are two ideals of a ring Ideal Test:A nonempty subset A of a ring is an ideal of…