Find the standard matrix for the following transformation t : r4 → r3: t(x1,x2,x3,x4) = (x1 −x2 +x3 −3x4,x1 −x2 +2x3 +4x4,2x1 −2x2 +
x3 +5x4)
(a) compute t(e⃗ ), t(e⃗ ), t(e⃗ ), and t(e⃗ ).
1234
(b) find an equation in vector form for the set of vectors ⃗x ∈ r4 such
that t (⃗x) = (−1, −4, 1). (c) what is the range of t?

its a straight line parallel to the time axis

a

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

mnkjn

step-by-step explanation: