1 3 9 2 0 3 -4 1 2 2 3 0 Let b = 3 and let A = 1 Is b in the range of the linear transformation 3 4 5 * → Ax? Why or Why not?

Q: 14. Let L: R2 → R2 be a linear transformation for which we know that L ([1 1]) = [1 -2], L ([-1 1])…

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Q: 3. Let L: R R' be the linear transformation defined by L(X) = Ax, where A is a 3 x 3 matrix with no…

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Q: 4. Consider two 3 × 3 matrices A and B with det(A) = -2 and det(B) = -1. Let T(*) = Až be a linear…

A: solution :-

Q: A linear transformation T : R* –→ R? whose matrix is -3 3 6 -2 2 3+ k is onto if and only if k +

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Q: 6. Suppose T: R² R² is a linear transformation such that ¹(B)-1(B)-1) T and T Find 7 ([^]). T

A: A detailed solution is given below

Q: 10. Suppose that T: R3 → R+ is a linear transformation with T(1,0,1)-(1,2,0,1), T(1,1,0)=(2,1,1,0),…

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Q: For matrix transformation T(x) = Ax, the rank of transformation T' is the same as the rank of matrix…

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Q: Let T be a linear transformation from M. M2,2 into M. such that 2,2 ((::)-[::} (::)-[: } 1 -1 0 1 0…

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Q: Which of the following is NOT a linear transformation? O Let V be the set of n x n matrices and L :…

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Q: Let L: R3 R2 be a linear transformation for which we know that L L L. (a) What is L -2

A: Given: L:R3→R2 be a linear transformation for which we know that  L100=2-4, L001=3-5, L001=23

Q: QUESTION 2 X1 X1-2 is a linear transformation. 2 T: R? → R² defined by T X1-4x2] メ2 True False

A: Concepts:

Q: -1 1 3 9 0 3 1 2 -2 3 0 3 and let A = 1 Let b = -1 -4 Is 6 in the range of the linear transformation…

A: According to the given information it is required to check if the given vector b lies in the range…

Q: () - ) 13 + 11 Let L R → R³ be the linear transformation defined as Lx2 x2 + x1, then dim(ker(L))…

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Q: 3. Determine whether the linear transformation x → Ax = (x + x2 + x3,x1+ x3, x2 – 13), x = (*1, x2,…

A: Use matrix determinant to find invertibilty of given linear transformation and also find matrix…

Q: d the B-matrix for the transformation XHAX when B= {b1, b2, b3}. 9 - 88 -22 - 4 - 3 4 A = 1 19 b1 1…

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Q: Suppose that T :P2 → R² is a linear transformation. If B = 1 2 {1, x, x²}, D = {(1,1), (–1, 1)}, and…

A: First option correct.

Q: a. Suppose T is a linear transformation such that 1 T 2 = |1,T 3 -6 3 -2 Find A such that T(x) = Ax.

A: a. Given the following transformations: T12-6=513, T-1-15=115, and T0-12=53-2. Let A=abcdefghi. Now,…

Q: If L:R2→R² is a linear transformation defined by CH -8 u, +9 uz -8 u2 then the standard matrix…

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Q: 2 4 1 Let T: R2 → R³ be a linear transformation for which T and T -1 1 7 and T 4 Find T a 4 :) - a…

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Q: If L:R2→ R² is a linear transformation defined by then is equal to O (-33 3 26 33 26 O None of the…

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Q: (4) Let B be the matrix 1 1 3 В - 2 4 -1 -3 1 -6 -2 and let TB : R“ → R³ be the linear…

A: The given transformation is not one-to-one.

Q: 3. Let L: RR be the linear transformation defined by L(x) = Ax, where A is a 3 x 3 matrix with no…

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Q: 8. For each of the linear transformations below, write the matrix of the linear transformation. […

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Q: -1 3 and let A be the matrix in Exercise 10. Is -1 Let b = 4 b in the range of the linear…

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Q: [1-4 7 -5] and let A = 0 1 -4 3 L2-6 6 –4] Let b = Is b in the range of the linear transformation X…

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Q: [:) -9 4 4 Let A = 6 -4 4 Define the linear transformation T : R³ → R? as T(x) = Ax. 5 a Find the…

A: We have to find the matric

Q: b. Let T be a linear transformation induced by the matrix A = and S a linear transfor- mation…

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Q: T : R2 [x] - → M2x2 (R) is a linear transformation which satisfies 2 1 4 .If 10 1 1 ,T(x)= 1 T(1) =…

A: We use the definition of linear transformation to find the value of  a11+a22-a12-a21.  For a linear…

Q: Which of the following is NOT a linear transformation? (:) - [-) L: R² → R2 defined by L Let V be…

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Q: Let L: R? → R be a linear transformation withL (1,0) = then L(2, 4) is 3 and L(0, 1) = 2, O 14 O 8…

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Q: 6. Let LR³ R₂[r] be a linear transformation such that LO 2 L0=1+x². Calculate L 3 (1) (b) x² + 5x +…

A: Let L:ℝ3→ℝ2[x] be a linear transformation such that L100=x+x2,L010=1+xand L001=1+x2.

Q: 10. Supposed that T: P»P, be a linear transformation where T(1) = 1+ x*, T(x) = x² – x³, T(x³) = 2 +…

A: 10 Suppose that T→P2→P3be a linear transformation where T1=1+x2, Tx=x2−x3 and Tx2=2+x3 We have to…

Q: 2, 2 If T:R? → R' is a linear transformation with T 4| and T then: "(:) - 15 T 3

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Q: 7 u - 8 uz Determine whether the function L:R2+R2 defined by L is a linear transformation, or not.…

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Q: 3. a) Is there exists a linear map T: R2 R2 for which T(7,7)=(4,-5) and T(2,2)=(8,-2)? Justify your…

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Q: If L:R2→R? is a linear transformation defined by CH 6 uz +7 u2 -7 u, +3 uz. then the standard matrix…

A: A multiplication of two matrix is given

Q: Suppose T is a linear transformation, where (1, – 1, 1) T(u) T(7) (1, 0, 0) %3D (0, 1, 0) (3, – 5, –…

A: Given: u→=1, 0, 0                            T(u→)=1, -1, 1v→=0, 1, 0…

Q: 4 If T: R? → R³ is a linear transformation for which T 3 and T and A is the standard matrix for this…

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Q: 4. Let L: R5 R¹ be a linear transformation, and let S R5. Suppose that {L(v₁), L(v₂), L(v3)} is…

A: The solution is given as

Q: Let L: R3 R2 be the linear transformation for which L(1,0,1)=(-1,3), L(0,-1,2)=(2,-1),…

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Q: - 16 Suppose T:R → R² is a linear transformation with T 10 3 - 5 | 141. - 14 Find the (standard)…

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Q: 2 9. If T:R? → R³ is a linear transformation with T 4 | and T then: 15 T 3

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Q: 5. Let L: R¹ R₂[r] be a linear transformation such that L0-r+2², L1=1+2 and 48 401 (1) -1+².…

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Q: Let S be a linear transformation from R? to R2 defined by -3 Let T be a linear transformation from…

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Q: 1. Let L: R R' be defined by L(r, y) (r - y,0, r+y). (a) Show that L is a linear transformation. (b)…

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Q: -29 If T: R- R' is a linear transformation such that T 10 and T then the matrix that represents 7 is…

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Q: If 4 2 R = 4 R is the matrix of a linear transformation consisting of a rotation with angle 0 and a…

A: Given the matrix R=4224. The rotation matrix is of the form R=rcosθrsinθrsinθrcosθ, where r is the…

Q: )A linear transformation T : R → R? whose matrix is -3 -6 -9 -1 -2 -4 + k s onto if and only if k #

A: A linear transformation T:ℝ3→ℝ2 whose matrix is      -3-6-9-1-2-4+k

Q: Let T: R? R3 be a linear transformation. Suppose T( 2 and T( 4 Find the standard matrix of T. -2 1 1…

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