Let T: ℝm → ℝn and S: ℝn → ℝp be linear transformations. Then S ∘ T: ℝm → ℝp is a linear transformation. Moreover, their standard matrices are related by [S ∘ T] = [S][T]. Verify the theorem above by finding the matrix of S ∘ T by direct substitution and by matrix multiplication of [S][T]. T x1 x2 = x2 −x1 , S y1 y2 = y1 + 5y2 2y1 + y2 y1 − y2

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step-by-step explanation:

the answer is b.

step-by-step explanation:

identity property is where 0+whatever number=whatever number. basically 0+ a number.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

a

step-by-step explanation: