Solve the following problems put it in word file save it as PDF file. 1. The probability distribution below shows the number of typing errors (x) and the probability p(x) of committing these errors whenever clerks type-in a document. Compute the variance and standard deviation. y 1 2 4 5 P(y) 0.02 0.11 0.42 0.31 0.10 0.04

Q: 8-9 Let A = 2 3 (a) Find 5A +6B. 5A +6B = and B= 9-2 Complete parts a through d.

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Q: 10. Simplify and express in terms of i: 5V-4 + v-I- 2/-9

A: Answer is mentioned below -

Q: 4 -5 - 2 – 2 1 1 3 Compute: 2 5 3 5 5 3 2 0 -2 4 3 Preview

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Q: 2 3 Use the substitution scheme and the matrix 1 4 7 L2 3 61 Code the message "Engineering".

A: The below table is used for encrypting and decrypting messages. Alphabet A B C D E F G H I…

Q: x- y+10z = 29 x+ y+2=6

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Q: -4 -4 -1 1 -2 If A = 5-5 and B compute AB and BA, if possible. -2 -1 -2 -1 -4

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Q: 6. What 3 x 3 matrix exchanges rows 1 and 2, but leaves row three alone?

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Q: [ 5 8 . Determine x and y if: ]3 4] 23 34

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Q: 4 -2 1 -2 A = -3 1 -2 3 1 -1 -1 determine the following entries: a32 = a21 = a13 %3D

A: Given matrix is A = 4-21-2-312-231-1-1

Q: Find Reduced Row Echelon Form

A: Solution: The objective is to find the row reduced echelon form of the given matrix

Q: 1 -4 -2 B = |0 3 2 0 1 2. A = -1 4 1 -1 2 0 1 4 Find: 1: A.A1-B2 2: BT.B1+A?

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Q: 1. Perform the following operations A+B A - B 2A-B A = 32- -11 [0 2 1] 5, B = 5 4 2 2 1 0 2 4 0 1 2

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Q: 8 -9 9 -2 LOMA- [2 ²3] and B-[37] Let = B= 1 (a) Find 5A + 6B. 94-57 5A +6B = 28 21 (b) Find 6A-5B.…

A: Addition and subtraction of Matrices

Q: 5. Find 5A-3B. [6-5 8 [7 5-61 B 4 3-4 5 -4 3

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Q: |h -4 -2 10 h -9 4 Find an LU factorization of A=| 0 h=102 -4 0 1 4 4 h/2

A: A=102-4-210102-94200-42014400051 In this problem, we have to find matrices L(lower triangular) and…

Q: – 4 1 -2 2 Compute:

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Q: 2 1 -1 1 -2 3 2 1 -1 -2 1 3 2 -1 1 2 2 If A = show that -2 1 (A +B)² A² + AB + BA + B² %3D

A: Given, A=21-11-23-212 , B=1-12-2132-11

Q: 4 -2 Compute A - 213 and (213 )A, where A = -3 2 - 5 - 4 A- 213 =D 4- 2. 2.

A: Consider the given matrix as, 4-24-32-5-422

Q: x-7 y = 4 3. X-9y-4

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Q: X = A + 3B, 1 A= -1 0 5 -1 -1 -4 3 2 2 B= 1 -2 -2 -3 3 -3 3-5 X = 2(AB+C), (1 2) (:)-(C) B= 1 0, C=…

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Q: 3 . If 4C + 2 [10 0 , find C. 4 2

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Q: (3+5i)- (2-1)- 1+6i o 1-6i 6+i 2-4i C

A: When two complex number are added, the real parts are added with each other and the imaginary parts…

Q: If v-28 is subtracted from V-63, the difference is A i B B iv7 © -iv7 V-35

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Q: O Multiply O x+1 ○2-5 I I x-+-5 3x+2 x+4 2x-11 x+3 2x²-7x-15 x²-25 x x²+x 2x2+5x+3

A: We need to multiply2x2-7x-15x2-25×x2+x2x2+5x+3

Q: 4 -3 0 Let A = 3 -2 0 Diagonalize A and find A231. -4 2 -1

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Q: X = A +3B, 1 A= -1 5 -1 2 0-3 X = 2(AB+C), A= 2 , B = 1 3 -3 (30-1 (1 2) +4)-(3-49 B= 1 0, C= 0 6…

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Q: [1 -2 -1] Let A- 2 4 l3 0 -2 -1 3 and B- 3 2 . Express the second column of AB as linear…

A: The objective is to express the second column of AB as linear combinations.

Q: Compute: -57 5 + [ 5 0 -1

A: Given data

Q: Find BA. A= BA= 0 -:] 7 -1 -3 0 -3 -5 -4

A: Finding the product of matrices.

Q: Let 4 1 - 3 -2 -9 and 1 A =| - 3 В C =| 0 3 Prove that 5 - 2 -1 1 1 – 4 | (BA)" – A" B" + AC = AC,…

A: (BA)T - ATBT + AC = AC In LHS, We know that, By the properties of Transpose, (BA)T = ATBT .…

Q: -5 1 -5 Let A = -4 ,B = -5 -1 3 1 Compute: 4AT + B

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Q: Multiply. (z-4)² O None of these Oz²-82-16 z² +8z+16 Oz² +16 z²-16

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Q: -4 -1 1 Identify the elements on the main diagonal. 11 2 0 5 -6 -7

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