Find the value of k for which the matrix A = [2 -5 9 -1 3 -5 7 1 k] has rank 2. k = .

k = 13

Step-by-step explanation:

Matrix is;

A =

[2 -5 9]

[-1 3 -5]

[ 7 1 k ]

Number of unknowns is less than the rank of 2. Thus, the determinant has to be zero for us to find k.

Thus, we have;

2((3 × k) - (-5 × 1)) -(-5)((-1 × k) - (-5 × 7)) + 9((-1 × 1) - (7 × 3)) = 0

Simplifying further gives;

2(3k +5) + 5(-k + 35) + 9(-22) = 0

6k + 10 - 5k + 175 - 198 = 0

k - 198 + 185 = 0

k - 13 = 0

k = 13

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.