Q1.One of the following is correct (a) are basis for the S(R’) (b))| are basis for the S(R²) and and (c) and are basis for the S(R) (d) ) and are basis for the S(R')/ (e)bll the above 2.Let I' be a vector space of all n by n diagonal matrices, then the dimension of V is (a) n? (b) n² – n (c) n² +n (d) - 2.

Q: 9. True or False (T/F): If True, Prove it; If False, give a counter-example. a) For all nonzero nxn…

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Q: C: Let T be the linear operator associated in the standard basis B of F2 with the matrix 2 - [34] -2…

A: C. Given that be a linear map whose associated matrix with respect to standard basis  is    .In…

Q: 2. Find a vector orthogonal to the nullspace of the matrix [1 27 6. 4 L5 -1 2.

A: According to the given information it is required to find a vector orthogonal to the null space of a…

Q: Consider the linear operator D : P3 (R) → P3 (R) defined via the deriva- tive: D (f) = f'. Find the…

A: Given linear operator is D : P3ℝ→ P3ℝ defined via the derivative: Df=f'.   To Find: The matrix…

Q: Consider the 2 X 2 matrices A1 =  1      1           A2 =  0      1        A3  =   0      0      A4…

A: Thus, the four matrices are not linearly independent.

Q: : Which of the following statements are always true? (1) The set {1, x,x} spans P2 (ii) In M, the…

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Q: X2 X₁ + X₂ x2 64-B be bases for R2 and R³, respectively. (a) Compute MȚ(B, B'), the matrix of T with…

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Q: 3. (a) Suppose that T: VV is a linear transformation, where V is a vector space of dimension n. If B…

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Q: 2yy" = 1 + (y')² 2

A:

Q: .

A: Given two bases of R2:

Q: Let T = (tij) be the 7 × 7 matrix with (i, j)-entry tij given by 1,1 ≤ i ≤6, tij 0 for all other i,…

A:

Q: Example 3: Find the coordinate matrix of x (3, 19, 2) in R³ relative to the basis B' = {(8, 11,0),…

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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: Let T : R" → Rm be a linear transformation. Describe how to find a basis B for Rn and a basis C for…

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Q: Which of the following sets are closed under scalar multiplication? (i) The set of all matrices in…

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Q: Let T(-) be a linear invertible transformation mapping vectors in R³ to vectors in R³. The vectors…

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Q: 3. Let T be a linear operator in C² and is defined by T(a, b) = (3a + (2 + i)b, (2 — i)a + 7b) (a)…

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Q: Let matrix T be T= [124] 364 and let vectors u and v be u= 0 For each of the vectors determine…

A: We have , T = 121364 We need to determine null space of matrix T. For that , first we will find…

Q: 4. Let T₁(x) = A₁ (x) and T₂(x) = A₂(x) be defined by the following matrices A₁, A2. Let T = T₂0 T₁.…

A: Given that, a) A1=-201315, A2=3012, x=3-21 b) A1=1111, A2=23-45, x=13. We have to find the matrix…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.