Kiili Making

ASSIGNMENT

Question No: 2

3^2×9^(1/2) 〖÷27〗^(-4/3)

3^2×3^(2(1/2)) 〖÷3〗^(3(-4/3))

3^2×3^1 〖÷3〗^(-4)

3^((2+1)) 〖÷3〗^(-4)

3^3 〖÷3〗^(-4)

3^(3-(-4))

3^7

√(〖64〗^2 )/8^(2/3) ×4÷1/128(√256)

〖〖64〗^2〗^(1/2)/8^(2/3) ×4÷1/128(〖256〗^(1/2))

2^((6)(2)(1/2) )/2^3(2/3) ×2^2÷1/2^7 (2^8(1/2) )

2^6/2^2 ×2^2÷1/2^7 (2^4)

2^(6+2)/2^2 ÷(1(2^4))/2^7

2^8/2^2 ÷2^4/2^7

2^(8-2)÷2^(4-7)

2^6÷2^(-3)

2^(6-(-3))

2^9

=514

((2〖xy〗^2 )^3×3x^(-2) y)/(3x^3 y×2y^6 x^(-2) )

((2^3 x^(1)(3) y^(2)(3) )×3x^(-2) y)/(3x^3 y×2y^6 x^(-2) )

((2^3 x^3 y^6 )×3x^(-2) y)/(3x^3 y×2y^6 x^(-2) )

((2^3 )(3) x^(3+(-2) ) y^(6+1) )/((2)(3) x^(3+(-2) ) y^(6+1) )

((2^3 )(3)xy^7 )/((2)(3)xy^7 )

(2^(3-1) )(3^(1-1) ) x^(1-1) y^(7-7)

(2^2 )(3^0 ) x^0 y^0

(2^2 )(1)(1)(1)

=2^2

2x^4 y×4^(-1) x^3 y^(-2)÷8x^7 y

2x^4 y×2^((2)(-1)) x^3 y^(-2)÷2^3 x^7 y

2^(1+(-2)) x^(4+3) y^(1+(-2) )÷2^3 x^7 y

2^(-1) x^7 y^(-1)÷2^3 x^7 y

2^(-1-3) x^(7-7) y^(-1-1)

2^(-4) x^0 y^(-2)

2^(-4) (1)y^(-2)

2^(-4) y^(-2)

∛(x^(3/2) ) × ((〖4x〗^(-2)+y/x)/(〖3x〗^(-2) y^3 )) ÷ (x^(-1/2)/2y)

x^((1/3)3/2)× ((〖4x/x〗^(1+(-2))+y/x)/(〖3x〗^(-2) y^3 )) ÷ (x^(-1/2)/2y)

x^(1/2)× ((〖4x/x〗^(-1)+y/x)/(〖3x〗^(-2) y^3 )) × (2y/x^(-1/2) )

x^(1/2)× ((〖4x〗^(-1-1)+x^(-1) y)/(〖3x〗^(-2) y^3 )) × (2y/x^(-1/2) )

x^(1/2)× ((〖8x〗^(-2) y+〖2x〗^(-1) y^2)/(〖3x〗^(-5/2) y^3 ))

((〖8x〗^(-2-(-5/2)) y^(1-3)+〖2x〗^(-1-(-5/2)) y^(2-3))/3)

((〖8x〗^(-1/2) y^(-2)+〖2x〗^(-3/2) y^(-1))/3)

((〖8x〗^(1/2+(-1/2)) y^(-2)+〖2x〗^(1/2+(-3/2)) y^(-1))/3)

8/3 x^0 y^(-2)+2/3 x^(-1) y^(-1)

8/3 y^(-2)+2/3 x^(-1) y^(-1)

Question No: 3

A+B: In order to add two or more matrices the order of the matrix should be the same. The order of matrix A is (3×2) and B has an order of ( 3 X 3). Hence, the matrix cannot be defined.

B+A: In order to add two or more matrices the order of the matrix should be the same. The order of matrix B is (3X3) and matrix A has an order of (3X2). Hence, the matrix cannot be defined.

AB: In order to multiply two or matrices the order of the matrix is very important. The number of rows of the first matrix should be the same with the second matrix number of columns. The Matrix A has 2 rows while matrix B has 3 columns. Hence the matrix cannot be defined.

BA:

[■(1&5&2@-1&1&0@-4&1&3)][■(3&0@-1&2@1&1)]

[■(((1)(3) )+((5)(-1) )+((2)(1) ) @((-1)(3) )+((1)(-1) )+((0)(1) )@((-4)(3) )+((1)(-1) )+((3)(1) ) )■( ((1)(0) )+((5)(2) )+((2)(1))@ ((-1)(0) )+((1)(2) )+((0)(1))@ ((-4)(0) )+((1)(2) )+((3)(1)))]

[(■((3+(-5)+2)@-3+(-1)+0)@(-12+(-1)+3))■((0+10+2)@(0+2+0)@(0+2+3))]

[■(0@-4@-10)■(12@2@5)]

A^T A

A=[■(3&0@-1&2@1&1)]

A^T= [■(3&-1&1@0&2&1)]

[■(3&-1&1@0&2&1)][■(3&0@-1&2@1&1)]

[■((3)(3)+(-1)(-1)+(1)(1)&(3)(0)+(-1)(2)+(1)(1)@(0)(3)+(2)(-1)+(1)(1)&(0)(0)+(2)(2)+(1)(1))]

=[■(9+1+1&0+(-2)+1@0+(-2)+1&0+4+1)]

[■(11&-1@-1&5)]

CD:

[■(3&-1@2&1@4&3)][■(4&-1@2&0)]

[■((3)(4)+(-1)(2)&(3)(-1)+(-1)(0)@(2)(4)+(1)(2)&(2)(-1)+(1)(0)@(4)(4)+(3)(2)&(4)(-1)+(3)(0))]

[■(12+(-2)&-3+0@8+2&-2+0@16+6&-4+3)]

[■(10&-3@10&-2@22&-1)]

DC: In order to multiply two or matrices the order of the matrix is very important. The number of rows of the first matrix should be the same with the second matrix number of columns. The Matrix D has 2 rows while matrix C has 3 columns. Hence the matrix cannot be defined.

D^2=(D)(D)

[■(4&-1@2&0)][■(4&-1@2&0)]

[■((4)(4)+(-1)(2)&(4)(-1)+(-1)(0)@(2)(4)+(0)(2)&(2)(-1)+(0)(0))]

[■(16+(-2)&-4+0@8+0&-2+0)]

[■(14&-4@8&-2)]

A^2= [■(a&b@c&d)][■(a&b@c&d)]

=[■((a)(a)+(b)(c)&(a)(b)+(b)(d)@(c)(a)+(d)(c)&(c)(b)+(d)(d) )]

A^2=[■(a^2+bc&ab+bd@ca+dc&cb+d^2