Answer the following questions. You do not need to justify your answers. (a) Let X be the set of all 3×3 matrices whose diagonal entries are all 0. With the usual matrix addition and scalar multiplication, is X a vector space? (b) Let Y be the set of all 3 × 3 matrices whose diagonal entries add up to 0. With the usual matrix addition and scalar multiplication, is Y a vector space? (c) Let Z be the set of all polynomials of degree exactly 5. Is Z a vector space? Show all your work! continued on next page 1 2 DUE 11:00PM, FRIDAY, JUNE 5 (d) Let V be the set of all 3×3 matrices whose determinant is equal to 0. With the usual matrix addition and scalar multiplication, is V a vector space? (e) Let W be the vector space of all lower triangular 4×4 matrices. What is the dimension of W?

15

step-by-step explanation:

we are given the following expression and we are to solve it and find the product:

-13 × (-5)

solving the given expression in the standard order of solving a mathematical expression, beginning with the opening of brackets and then multiplying the terms and changing their signs.

-3 × -5 = 15 (answer is positive because when negative is multiplied with negative, it gives a positive answer)

5.25 ounces

step-by-step explanation:

divided 3/4 and 6

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf = 

pf = 6,25 u

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step-by-step explanation:

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation: