Suppose that T is a linear transformation from R2 to the space of 2 × 2 matrices which satisfies: T((1, 1)) = [} 1 3 T((3,-2)) = What is T(2,4)? HINT: Note that - 2 (2,4) = 10(1,1) - (3,-2)

Q: find the inverse matrix

A: As per the question, we have to form a 3×3 matrix, given the unique symmetrical elements of YBUS(s)…

Q: [a11(t) a12(t) 1) Let A(T) = be differentiable. %3D Show that: d (det (A(t)) = det a 12 (t)] la21(t)…

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Q: 13. Using the transformation matrix, the result of mirroring the rectangle (0,0), (2,0), (2,2),…

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Q: Find u and usuch that the null space for the matrix U= 3 v= 0 -2 1 1 -3 -15 1 - 9 1 is span{u, }.

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Q: Find the matrix A of the linear transformation from R to R' given by 5 T 6 x1 + -1 x2. %3D -8 7 A =

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Q: (a) Construct the 3 × 3 matrices A₁ and A₂ associated to the linear transfor- mations L₁ and L2,…

A: (a)Two Linear transformations are mentioned:.Thus the matrix for the transformation  is given by and…

Q: The linear transformation_T:R³ OK² is represented. by the matrix [T]8= 1 20 where B= 012 and B' = 二…

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Q: Find the standard matrix for the linear transformation T. T(x₁, x₂) = (0, 0) ↓↑

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Q: 3. Show that (AB)* B' A' by using the matrices A and B giver [8 -2 5] 1 -5] B = 7 0 -3 A =1 -4 3 6.…

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Q: Consider the bases of R2 B1={(1,0),(1,3)} B2={(0,1),(1,1)} E={(1,0),(0,1)} Correspond M(Id)_B1_E (a…

A: To find a base change matrix from B1 to E, we need to find the linear combination of basis vector in…

Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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Q: The matrices A₁ = [J]. - [ ] 4-[61] , 10 form a basis for the linear space V = R²x2. Write the…

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Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

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Q: Find the transformation matrix for the following figure: B'(-5,3) A(-5,0) C(-3,0) B(-5,-3) A(-3,-3)

A: Given the triangle A(−3,−3),B(−5,−3),C(−3,−6).We need to find the transformation matrix so that we…

Q: Write the standard matrices of the given linear operators: a) L1(x) = (X1 +x2, X2 – X1) b) L2(x) =…

A: a. we have L1(x)=(x1+x2,x2-x1)  we take standard ordered basis β= (1,0),(0,1) and β=…

Q: Find the general form of the span of the indicated matrices. (Use only x and w as variables in your…

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Q: *(})- (;) -(;) 1 3

A: T:R2→R3 satisfying the condition, T11=121 and T12=132

Q: Let T: R² → R³ and S: R³ → R² be two linear transformations. Suppose the matrix of T is 21 -1 and…

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Q: then the standard matrix of T is A = IfT: R² R³ is a linear transformation such that - 22 19 -5 18…

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Q: If T: R" → R" m is a linear transformation and A is the standard matrix of T, then the size of A is…

A: Matrix

Q: For the​ matrixA=daig(-2,-1,2), put the following values in increasing​ order: det(A),​ rank(A),…

A: Given the matrix A=daig(-2,-1,2) is diagonal matrix Therefore the eigen values of A are -2, -1, 2.

Q: Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix…

A: As per guidelines of bartleby we solve only first three parts.

Q: why no matrix exists for one-to-one linear transformation from R^4 to R^3

A: Given: We have to prove no matrix exists for one-to-one linear transformation from R4 to R3.

Q: Use matrix multiplication to find the contraction of (a,b) with factor k =1 / alpha, where alpha is…

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Q: Write f= x + 10x1x2 + x3 as a difference of squares, and f= x? + 10x,x2 + 30x as a sum of squares.…

A: Given f=x12+10x1x2+x22.  Let the associated matrix of f be A=abba is 2×2 symmetric matrix. Then,…

Q: [102] 6. Find the kernel of the linear transformation whose standard matrix is B= 215. [237]

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Q: 3. For each of the following pairs of ordered bases ẞ and ẞ' for P2(R), find the change of…

A: To find the change of coordinates matrix from a basis β′ to β for the vector space VThe identity…

Q: (a) Show that the jth column of the matrix product AB is equal to the matrix product Ab;, where b;…

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Q: (1 point) The matrices - [8]. [J]. -[i]·.^ - [i]· A A4 = A₁ = A3 = A₂ = form a basis for the linear…

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