Question # 7: Find an LU factorization of the following matrices а. 1 4 -1 7 -2 1 6. 3 -2 -3 -4 -1 -1 7

Q: snip

A: The inverse of 2×2 matrix A=abcdis A-1=1Ad-b-ca. Consider the matrix A=3121, The determinant of A is…

Q: 1x?x+y SS (x +2y + 4z )dzdydx 0 x x-y

A: Explanation of the solution is given below...

Q: Community property of multiplication (a+b)(b+c)

A: We find commuting product of multiplication of -  (a+b) (b+C).

Q: Simplify the expression. (a b (a + b²)

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Q: B D E (i), (vi) (iii), (v) (iii), (iv) (iii), (vi) (i), (iv) We know the order of A3 is 3. Determine…

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Q: K-I -1 -1 %3D

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Q: (4 -1 1 (b).| 3 7 - 2 X2 1 3 1 II

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Q: L-1 1 (s²+1)³

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Q: 3x2+2x x2-6x Determine the non-permissible value(s) for Ox + 0, x # % Ox + 0, x + 6 Ox + 6 Ox + 0, x…

A: The function is given by 3x2+2xx2-6x To evaluate : The non-permissible values of x

Q: 6x 4x 7x + 40 Compute 7. O6+ 80 + C O 3x + 4x - 7In]x| + 40 + C O 18x+ 8x - 7 +C 2x O 3x + 4x-7in|x|…

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Q: Expand and simplify. (c) (x+2)3

A: According to the question,we have to expand and simplify x+23. As the above expression is algebraic…

Q: Evaluate L- { 3 2s (s+2)² (s–2)*

A: we need to determine the laplace invesreℒ-132s-3s+22+ss-24

Q: x² –1 4. x2 -4 (-2, – 1], [1,2)

A: Given :

Q: Using binet square find the value of F3+F7+F13

A: We have to find the value of F3+F7+F13 using Binet Square. Binet Square or Binet's Formula: Binet's…

Q: Find the inverse of T = 3 1 -1 - 1 2 2 2 2 1

A: Given matrix is,

Q: 3x +3x-5x² +x-1 dx x² +x -2 Q4 Evaluate

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Q: Find the rank(A) and null(A). 1 -3 -1 9 . -6 -1 4 -2 -10 -3 9. -6 -6 -3 3 -9 4 9 a) 1; 4 b) 2; 3 c)…

A: Rank(A) and Nullity (A)

Q: - 4x, + 2x, = -6 3x, - 5x, = 1 %3D

A:

Q: I +3 Evaluate – 1)²(z² + 2) dr.

A: Use partial fraction to write the integrand in different fractions.…

Q: B. DECODE 13 19 10 -1 -33 -77 3 -2 -14 4 1-9 -5 -25 -47 4 1-9 1 2 2 4433 A = 7 9 -1 -4 - -7]

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Q: 03 -5 141 o A+B 6. 2. L-2 3 -2

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Q: Show that A CB does not imply |A| ≤ B.

A: Answer :   To show that A ⊆ B does not imply |A| ≤ |B|, we can construct a counterexample. Consider…

Q: x1 X2 x 3 X4 +s +t 4x1 -X1 3x1 - 3x1 -5x2 +4x3 +3x4= 2 +x2 +3x3 +3x4 2 -4x2 +7x3 +6x4 = 4 +3x2 +9x3…

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Q: Example 6

A: The scores of the second attempt is given as- Second attempt 34 31 37 32 40 32 44 37 47 41…

Q: a) + )- (2x2 - 3x) = x² + x- 2x – 3x = (x² – 2x) + (x- 3x) = -x² - 2x

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Q: Solve the following recurrence relation with the given initial condition: an = (n + 1)a,n-1 for n =…

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Q: 3 2uv 2uv

A: Definition used -        We know -                          a0=1aman=am-n

Q: Determine the simplified form of 5+j4 5-j4

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Q: L-1 | 53 5 = 3s +1 3 – s2 + s - 1

A: Find the inverse Laplace transform of 3s+1s3-s2+s-1. Rewrite the denominator:…

Q: 3x2 + 5 dx. x2 – 3x +2 Evaluate

A: Integrate∫3x2+5x2−3x+2dx

Q: a+1/b = a-1/b + b+1/a

A: Given: a+1/b = a-1/b + b+1/a

Q: A D E (i), (vi) (iii), (v) (iii), (iv) (iii), (vi) (i), (iv) (ii) We know the order of A3 is 3.…

A: