By D. E. Littlewood

ISBN-10: 0486627152

ISBN-13: 9780486627151

**Read or Download A University Algebra: An Introduction to Classic and Modern Algebra PDF**

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**Extra info for A University Algebra: An Introduction to Classic and Modern Algebra**

**Example text**

1, 1 > _ 0 , - 8, - 7 _ _1> 7, 3 _ 3, 5, 7, 8 _6» 5, 4, 2_ Find the reciprocals of the matrices 4. f l , 1“ |. 5. ~ l, 1> 1“ 1, 2, 3 L l . 2_l * _ 1 , 3, 6 _ 9 6. ~1, 1, 1,2, 1, 3, __1, 4, 1, 3, 6, 10, 7. “ 2, 2, 1-1 n 4 - 2, 1, 2 10 > _ 1 , - 2 , 2_ 20_ Solve the following systems of equations by finding the reciprocals o f the matrices of coefficients. 8. x + y + 2z = a, 2x — y + 3z = b9 Zx + 2y — z = c. 9. 2x Zx 4x x -f + + — 3y 4y y y + 4z + z -f*2z + z -f- w -j- 2w -f- Zw — w = = = = a, bt c, d.

62/, x — y, n 0_ + 4. 1, 5, 3, 7, 3, 2, 4, 5, 2, 0, 4, 6, 4-| 1 7 10_ - 4, * + 10, 0, — 4, 6, * + 1, _ 0, - 10, 21, r $y, y, 0, 3x + - ’ y, r z , to — V, l, _ 2. 1 a:, 0, — x, in 1 2 0_ Oi 0, 3. ~ 3, 1, 0, 2, 1 1. ro, 1, 1, o, 3, 1, _1, 1, - — Z x — Z y, Z y, 2x + y , x 0, + 5y , an 2 ’ — x + y — 2 x — y — x — by 0 The Transform o f a Matrix The set o f linear equations x = axx + bxy + cxz, y = a%c + b $ + c2z, z = azx + 63y + czz, may be regarded as the transformation from one frame o f reference to another concerning the coordinates o f a given point.

A; + ay + a2z + a3 = 0, a: + by + 62z + 6s = 0, x + cy + c2z -|- c3= 0. 20 A UNIVERSITY ALGEBRA 5. hx — 3y -f- 4z + Qw = 9, 2x + 5y — 6z — 2w + 7 = 0, x + 2y — 3z + 4w = 2, 3a; + y — 3z — 5w + 4 = 0 Which of the following sets of equations are consistent ? 6. x + y + z = 1, x + 2y + 3z = 4, x + 3y -j- 6z = 10, x + 4y + lOz = 7. x + y + 2 = 1, x + 2y + 3z = 4, x -f- 3y -f- 6z — 10, x + 4y + 10z = + 3z = 4, x + 3y + 5z = 7, 8. x + y + z = 1, # + x + 4y -f 7z = 9. x + y + z = 1, a; + 2y + Sz = 4, x + 3y + 5z = 7, a; + 4y + 7z = 19 20 10 11 CH APTER II MATRICES Inner Products Consider the linear form $ = ax + by + cz + dw.

### A University Algebra: An Introduction to Classic and Modern Algebra by D. E. Littlewood

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