Let A = {a, b, c, d} and let R and S be the relations on A whose matrices are (1 0 1 0) 1 0 0 1 1 0 1 0) 0 1 0 1 and Ms . Find the matrices of 1 0 1 0 0 1 1 0 0 1 0 1) 0 10 1

Q: Let R, and R2 be relations on a set A represented by the matrices 1 01 1 and MR2 [1 1 01 MR. 1 1 1…

A: The matrix of the composition of relations is calculated as the productof matrices.

Q: Let Rj and R2 be relations on a set A represented by the matrices To 1 o' 0 1 1 Го 1 0 and MR2 1 0 0…

A: Given: MR1=010111100 and MR2=010011111

Q: If A and B are n X n matrices, prove the following properties of the trace: (a) tr(A + B) = tr(A) +…

A: Let A=[aij] and B=[bij] be n X n matrices. Let C=A+B and D=kA where C=[cij] and D=[dij] are n X n…

Q: 1 d) The set of all 2 × 2 matrices of the form 0 1 a (a E R) with usual matrix addition and scalar…

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Q: Let A = {1, 2, 4, 5} and B= {2, 4, 6}, and let the relation R from A to B be defined by xRy iff x <…

A: Option (b) is correct.

Q: Which of the following matrices shows that (3, 2) belongs to the relation it represents? (Select all…

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Q: and MR2 and R,be relations on a set A represented by the matrices MR. Let R1 0 11 100 R, = [1 0 1] 0…

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Q: Let Rị and R2 be relations on a set A represented by the matrices [o i o° | 1 1 1 1 0 0 0 1 1 1 MRI…

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Q: Let R1 and R2 be relations on a set A represented by the matrices ГО 1 Mr1 01 1 and Mr2 1 01 0| 1.…

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Q: Consider the matrices 0 7 0 8 0 0 0 0 1 4 13 -1 7 1 0 3 1 2 -1 25 -3 -19 1 -2 -1 A = 3 -6 1 1 1 and…

A: The main objective is to solve part a,cand d. In order to solve using the columns of A and using the…

Q: Let the linear map f:R3-R3 be defined by f(x, y, z)= (x – y – z, x + y, z – y). Then the third…

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Q: Let R1 and R2 be the relations represented in the matrix. [0 1 0 1] [1 0 1 1] 0010 0010 R2 1 100 1 1…

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Q: Let G : R? → R³ and F : R³ → Rª be defined by G( (x, y)) F( (a,b, c) ) (x +y, x – y, 2y) (a + b+ c,…

A: Given G:R2→R3 is defined as Gx,y=x+y,x-y,2y Also,  F:R3→R4 defined by Fa,b,c=a+b+c,2a+c,b+2c,a+b.

Q: Let R1 and R2 be relations on a set A represented by the matrices below: MR1 0 1 0 1 1 1 1 0 0 Mr2 =…

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Q: Let R,and R2 be relations on a set A represented by the matrices Mg, =10 0 0 1 ol and MR2 1 0 Find…

A: In this question, we have to find the product and composition of the relation matrix. To find the…

Q: Let R1 and R2 be the relations represented in the matrix. 1001 11 1 1 1 1 1 11 0 1 0 0 0 1 1 0 1 0…

A:

Q: If A and B are arbitrary real m x n matrices, then the mapping (A, B) = trace(A™B) defines an inner…

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Q: Let V = Mn,n (R) be the set of n x n real matrices. Let W1CV be the set of n x n upper-triangular…

A: Given that , V=Mn,nℝ is the set n×n real matrix. W1⊂V be the set of n×n upper-triangular matrix.…

Q: Let T : R² -> R² be defined by T ( 3x1 – 12 -1 B = 2 , and | . Let u = %3D -3x1 + x2. {{}} C = Given…

A: Consider the given information.

Q: Let P1, P2 E R"X" be two projection matrices (so that Pi = P; , P{ = P¡) with P1P2 = 0. Let the rank…

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Q: Let L be the linear operator on R³ defined by 2x1 – x2 – X3 L(x) = | 2x2 – x1 – X3 2x3 – X1 – X2…

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Q: Let T : P3 → R³ be defined by 2а — 2b + с — Зd -a + 36 + 2c – 3d . Let u = x – 3x. B = {1,x, x² , x³…

A: By using FTMR the answer is given as follows :

Q: Let W be a set of all 2 c 2 matrices of the form [ 0 a   b 0 ] , where V = M2,2 Prove that W is…

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Q: Let X be a set of 2×3 matrices. if for any a1 az az A = B = b1 b2 b3 b4 b5 b6 EX, a4 a5 a6 6 d(A, B)…

A:

Q: Let M be the vector space of 2 x 2 real-valued matrices. For M = [ a b c d] we define M# = [d b…

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Q: Let A = {a, b, c, d} and let R and S be the relations on A whose matrices are (1 0 1 0` 0 1 0 1 (1 0…

A: let A=a,b,c,d and let R and S be the relations on A whose matrices are  MR=1010010110100101 and…

Q: Let R1 and R2 be relations on a set A represented by the matrices below: MR1 = 0 1 0 1 1 1 1 0 0 Mr2…

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Q: Find all x in R* that are mapped into the zero vector by the transformation x-Ax for the given…

A: Answer is : X = (0 0 0 0) t

Q: Consider the set U of 2 × 2 matrices where all the elements are nonnegative. Is U a vector space? O…

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Q: -(:)- Let T : R? → R² be defined by T -2x1 + *2 2 B = Let u = -2x1 – 3x2 and C = 1 Given Pc ,use the…

A: Given T:R2→R2 defined by Tx1x2=−2x1+x2−2x1−3x2. Let u=2−4, B=31,21 and C=32,11 Given PC=1−1−23. We…

Q: Prove that T:P(x)→P,(x) defined by r(s(x)) - (x² -5x+ 6)f() is a linear transformation. Write the…

A: Given: To prove  T: P2X → P3Xf X →x2-5x+6 f '(x) Then the Basis of  P2X: α = 1+x, 1-xP3X: β =1, 1+x,…

Q: Let M₂ (R) be the set of 2 x 2 matrices with real number entries, i.e., b M₂ (R) = { [ a &] |…

A: The given matrix is M2ℝ=abcd: a,b,c,d∈ℝ To find : (a) M2ℝ is a ring under addition and…

Q: Let W be the set of 2x1 size matrices v=| y W is closed under scalar multiplication. Select one: O…

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Q: a T:R³ → V defined by T(a, b, c) =% ), where V is the set of all symmetric 2 x 2 matrices with…

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Q: Let A, P, Q be the matrices -1 1 1 1 -1 1 0 P = 2 Q = -1 1 3 -2 -1 0 1 0 0 0 1 0 0 3 -1 0 A = 1 1 B=…

A: Given : The matrices  P = 111211-110 , Q=-110-1113-2-1, A= 3-101114-3-1 and B = 010001000 To…

Q: Let B= {b1, b2} and c= {cl, c2} be bases for a vector space V, and suppose b1 = - cl + 4c2 and b2 =…

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Q: Consider the set U of 2 x 2 matrices where all the elements are nonnegative. Is U a vector space? O…

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Q: Let R1 and R2 be relations on a set A represented by the matrices [1 1 01 [1 1 01 0| and MR, MR, Lo…

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Q: Let A,B ∈Mn×n(C). (a) Prove that if B is invertible, then there exists a scalar c ∈C such that A +…

A: (a) Given: Matrix B is invertible.

Q: Each of the following matrices determines a linear map from R into R3: 2 0. 1 1. 2-1 (i) A = 2 -1…

A: Given that the matrices determines a linear map from . (i) Let the linear map is   given by, where…

Q: Given B = v1 {(0, 1, 1, 1)}, v2 = {2, 1, –1, –1} , v3 {(1,4, –1,2)} , v4{(6,9,4, 2)} B' = wi {(0,8,…

A: (b) T:R4→R3 is such that matrix Ais the transformation from B to B'. A=3-2101621-3071 Row reducing…

Q: 1. Let A and B be n xn matrices such that det A 0 and det B 0. Prove that ((AB)")-1 = (A-1)"(B-1)".…

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Q: Let U be an n x n matrix such that UT U=I. Show that U=+-1. (plus or minus 1)

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Q: Let A be the matrix defined by 1 A -3 | Let T : R? → R² be the map defined by T(x) = Ax. (b) M(T)…

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Q: 1. Let f(r) = ar +bx² + cz+d be a polynomial such that f(1) = 0, f(-1) = 12, f(2) = 12 and f(-2) =…

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Q: Let R1 and R2 be relations on a set A represented by the matrices below: Mr1 = 1 1 1 1 1 0 0 Mr2 = 0…

A: Given:

Q: Let V be the vector space of all (2 × 2) matrices. Determine whether the following matrices A, B,…

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Q: Let Mn(R) be the set of n x n matrices with real entries. Define the sets V1 = {A € M2(R) | A = A"}…

A: