For each of the following, factor the matrix A into a product QDQT where is orthogonal and D is diagonal. [5 1 1 8 (a) A = |1 -4 1 8 [588] .[?9] D -8 -2 (b) A = | –2 2 ܟܬ -5 5 200 ܩ -5 D 0 0 0 0 0

Q: Find the following products for p = (7,0, 2), q = (-2,2,-2), and r = (0,2,-3). a. (r p)q b. |p|l

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Q: Patricia derived the following incorrect formula by misapplying the Product Rule: a?y²) = x²(2y) +…

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Q: Find the product for (m-4)(m-3)

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Q: (2.1) Perform the indicated operations: a) (6 m² – 3 m³) (2m + n) b) (5x + 7y) + ( -5x + 2y) c) (2x…

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Q: = 7x3-3x2 +x+2 and B one: 5x3 +7x2-11 b. -5x3 +7x? – x - 11 -5x3 + x2 +x- 11 c.

A: Given: A=7x3-3x2+x+2B=2x3+4x2-9Find: B-A

Q: Find (x + 1)v2r2 + 4x + 6

A:

Q: f z-3x2- 4хy3 +6х,find. дудх

A: Given z=3x2-4xy3+6x we have to find ∂2z∂y∂x

Q: Question 13 Which of the following products is an example of 'Difference of Squares'? a3 +1 2? + 6x…

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Q: Find the product D (xD – 3) A) xD²– 2D B xD²+4D (c) xD² – 3D D xD²+3D

A: .

Q: A=[[3,2],[7,5]],B=[[2,6],[3,9]],AB=[[a,b],[c,d]] Determine the values of the entries in the product…

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Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: Compute (2i + k) × (3j + 5k).

A:

Q: (14+ x) ÷ 2 when x = 4

A: Note: It is being assumed that the expression: (14+ x) ÷ 2 needs to be evaluated when x=4.   In the…

Q: 4. Let -81 | A = 1 (a) Factor A into a product PDP-1, where D is diagonal. (b) Compute e4.

A: We can solve this using diagonalisation

Q: Evaluate the following:

A: Given that: ∫(6x2-4x+1)dx

Q: (y² + 2y + 18) ÷ (y+5)

A:

Q: - 1 2x -7y-2 4x2y-4 Simpify:

A:

Q: how do you write (14)(27)(523)(34)(1472) as a product of disjoint cycles

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Q: Find the inverse of AB if 5 -4 A-¹ and B-1 = = (AB)-¹ = -2 -4 14 -5 2 ]

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Q: find the value of 3y-3 given that -8y-9=7

A: Given,

Q: Find the LU factorization of A = A = 1 1 -3 0 9 3 -17 5 2

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Q: -1 -4 -1 5 21 A -2 -5 -14 4888|16 Find the LU factorization of A = A =

A:

Q: Calculate the triple product ā · (b x c), where ā =,b=, and č=.

A: Given vectors  a→=2 , -4 , 1b→=0 , 3 , -1c→=5 , -3 , 3

Q: Find the inverse of AB if 22 A and B-1 (AB)−¹ = = 5 3 2 -3 1 2 00

A: Recall: AB-1=B-1A-1

Q: Determine the conjugate of the product of, (3 – 2i) (4 + 3i)

A: solution:-3-2i4+3i=34+3i-2i4+3i=12+9i-8i-6i2putting i2=-1=12+9i-8i-6-12=12+9i-8i+6=18+i

Q: Find the inverse of AB if A-1 and -3 2 1 3 B-1 = -3 4 02 (AB)-1= [88]

A: Given: To Find: To determine .

Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

Q: Simplify (z+1)²(3xy²)3 (9y²) 2x-³(z+1)-1

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…

Q: Evaluate az+1)in(d.r+1)dr. 1 dx.

A: The integration function is ∫14x+1ln4x+1dx

Q: 2. (9Ax da

A: The given integral,∫-404.4x2-1 dx