(1) (20 points) let a be an n x n matrix. determine which (if any) of the statements are equivalent to the statement the matriz a is invertible. (a) the columns of a are linearly independent. (b) the columns of a span r". (c) the null space ofa is trivial, ie. nul(). (d) there is only one solution to the equation ax = 0 and it is the x = 0. (e) the unique linear map ta : rn ? rn, defined by a, is one-to-one. ) the unique linear map ta : rn ? rn, defined by a, is onto. (g) the rank of a is n. j (h) det a0.

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)

d .tv

step-by-step explanation:

the side tv is included in both triangles.   this means it corresponds to itself in the transformation.

this is justified by using the reflexive property, which states that anything is congruent to itself.

you should think about the answers you give and expect the same form your questions.