Linear Algebra Row Reduction

Linear algebra is a type of algebra that involves only one variable

. E.g. x + 2 = 5 is an example of linear algebra expression. Solving these expressions leads to row reduction at each step. Let us see certain examples that involve linear algebra ow reduction problems. Step by step solution to each example has been provided for your understanding. Some practice problems have also been given at the end of article.

Linear Algebra Row Reduction Examples

Ex 1. 5x - 3 = 7

Sol : 5x - 3 = 7

Adding 3 to both sides of equation

5x = 7 + 3

5x = 10

Dividing by 5 on both sides

x = 10/5

x = 2 Answer

Ex 2: 3(x - 1) = 5(2x - 2)

Sol : 3(x - 1) = 5(2x - 2)

3x - 3 = 10x - 10

Combining like terms

3x - 10x = -10 + 3

- 7x = -7

Dividing by -7 on both sides

x = (-7)/(-7)

x = 1 Answer

Ex 3: (5 - 3x) / (7 - 2x) = 2/5

Sol : (5 - 3x)/(7 - 2x) = 2/5

By cross- multiplying

5 (5 - 3x) = 2 (7 - 2x)

25 - 15x = 14 - 4x

Combining like terms

25 - 14 = -4x + 15x

9 = 11x

9/11 = x

or x = 9/11 Answer

Ex 4: n(2n + 3) - 2n(n - 5) = 6

Sol : n (2n + 3) - 2n (n - 5) = 6

2n2 + 3n - 2n2 + 10n = 6

Combining like terms, we get

2n2 - 2n2 + 3n + 10n = 6

13n = 6

n = 6/13 Answer

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Example Problems on Linear Algebra Row Reduction:

Ex 5: [k(3k - 2) - 3k (k +2)]/(2k - 3) = 8

Sol: [k(3k - 2) - 3k(k+2)]/(2k-3) = 8

By coss - multiplication, we get

k (3k - 2) - 3k (k + 2) = 8 (2k - 3)

3k2 - 2k - 3k2 - 6k = 16k - 24

Combining like terms, we get

3k2 - 3k2 - 2k - 6k - 16k = -24

- 24k = - 24

Dividing on both sides by -24

k = -24/-24

k = 1 Answer

Ex 6: [(2p + 3) - (5p + 7)]/ (6p + 11) = 10/23

So l : [(2p + 3) - (5p + 7)]/ (6p + 11) = 10/23

(2p + 3 - 5p - 7)/(6p + 11) = 10/23

(-3p - 4) / (6p + 11) = 10/23

By cross - multiplication, we get

23 (-3p - 4) = 10 (6p + 11)

- 69p - 92 = 60p + 110

Combining like terms,

-69p - 60p = 110 + 92

- 129 p = 202

Dividing both sides by -129

p = 202/ -129 Answer

Ex 7 : q/2 = 5

Sol : q/2 = 5

Multiply both sides by 2

q = 5 x 2

q = 2 Ans

Some Practice Problems on Linear Algebra Row Reduction:

1. x + 12 = 34

2. 9u = 81

3. 3x - 7 = 2x - 5

4. 7 (3x - 5) = 5 (4x - 7)

5. (2m + 4)/(3m + 13) = -4

by: mathqa

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