e) Let W = {(x; y) x,yER}. Define addition and scalar multiplication %3D a + B = (x; y) + (a ; b) = (x + a + 1; y + b -1) = k(x ; y) k a = (x +k; y) %3D = (a + B) + Y for a,B, Y e W a + (B + Y) 3 0 EW such that a + 0 = 0 + a = a, a e W k( a+ B) = ka + kß, a ß e W, keR a) b) c) %3D

Q: Explain the dimension of the row space.

A: The dimension of the row space is called the rank of the matrix. This is the same as the maximum…

Q: e down a polynomial of degree exactly 4 that interpolates the four points: (-1,-5 1), (2, 1), (3,…

A: We have to find the polynomial equation from given points.

Q: Find a polynomial y = p(x) of degree 4 that goes through the points (0, 4), (1, 2), (2, -4), (3,…

A: solution of the given question is like this:

Q: By evaluating the determinants, verify the addition rule for the 2 x 2 case: a12 a22 la21 a22 la21…

A: Determinate

Q: Which statement is NOT true? When using the conv command, the two polynomials have to be of the…

A: consider the equation

Q: [61] Diagonalize B = (by finding P and D) or explain why B isn't diagonalizable.

A:

Q: find the quadratic polynomial whose zeores are (I) 3,-4 (ii) 2,1

A: Given problem is : find the quadratic polynomial whose zeroes are (I) 3,-4 (ii) 2,1

Q: Formulate that the Lagrange interpolation polynomial that passes through points (0, 3), (1,4) and…

A: To show that the Lagrange interpolation polynomial that passes through points (0,-3),(1,4),(2,15) is…

Q: Multiply: 3y2(2y³ - 4y² + 5y) a. 6y5-12y + 15y³ d. 5y5-y¹ + 8y³ b. 5y6-y4+8y² e. 6y5-y4+ 15y³ c. 6y6…

A: SOLUTION-

Q: x + 3 -dx х — 1

A:

Q: 2) g(x)= -2 () 2x+1 Transformations: a= b= h= k=

A:

Q: Find the polynomials connecting the points (0,1), (1,3), and (2,13) ​​by quadratic interpolation.

A:

Q: the smallest possibl product of the two numbers x>= 0 and y<= 0, such that 2x-y=120 is:

A: Let x and y be two numbers such that  x≥0,y≤0, 2x-y=120y=2x-120

Q: Write g(x) = x² + x³ + 2x²+x+2 as a product of irreducible polynomials over 2.₂. за

A: Write as a product of irreducible polynomials over .

Q: The set of polynomials {1, x² + 3x“, 2x² – 7x4} is a linearly independent set in P4.

A: NOTE: Due to time limit answer of 1 is given here, for other please ask in a different question.…

Q: Evaluate determinant: 2 4 5 0 -1 2 3 -5 12

A:

Q: Let P0. (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, y1), (x2,…

A:

Q: Use row reduction to find 0 3 1 3 -3 . Demonstrate that your inverse is correct.

A:

Q: (3) Construct a linear spline interpolating (-1, 0), (0, 1), (1, 3).

A:

Q: if (A|b) is in reduced row echelon form, prove that A is also in reduced row echelon form.

A: (A|b) is the augmented matrix formed by placing elements of matrix B to the right of elements of…

Q: 7. Let T1, T2, T3 represent the following row operations: T₁: Interchange rows 1 and 3. T2: Multiply…

A:

Q: Find sub spaces row (A), column (A) and null (A). Find rank 103 A=015

A: first we shall find rank of the matrix then find row space, column space and null space

Q: Give the matrix representing the relation in the previous problem. Label the rows and columns.

A:

Q: 3. Find both linear and quadratic interpolating polynomials for the points (-2,-13) , (-1,-3) ,…

A: We take given pairs of points as (x, y) x y -2 -13 -1 -3 1 -1 2 -9 3 17 We have…