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Let T be the linear transformation whose standard matrix is Aequals[Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column negative

Scilla [17]

Answer:

Yes the linear transformation is one to one and it maps a set of real numbers R cubed onto set of real numbers R cubed

Step-by-step explanation:

To show that the linear transformation is one to one, we must show that the columns are linearly independent columns (i.e it must have the trivial solution)

$A = \left[\begin{array}{cccc}1&-2&3&0\\-1&3&-4&0\\-5&-2&9&0\end{array}\right]$

For the Augumented matrix A and applying Row Reduction Formula we have that

= $\left[\begin{array}{cccc}1&-2&3&0\\0&1&-1&0\\0&0&-18&0\end{array}\right]$

we can deductively see that $x_{3} = 0, x_{2} = 0, x_{1} = 0$

Since the columns are linearly independent, Hence it is a one-to-one transformation and it maps a set of real numbers R cubed onto set of real numbers R cubed

4 0

3 years ago

Read 2 more answers

The ratio of trumpet players to tuba players at a high school is 5:2 Which statement is true?

marysya [2.9K]

The given ratio is 5 trumpet players : 2 tuba players.

A. Since the ratio is 5:2, at the smallest ratio there would be 7 players total (5+2). So tuba players would be 2/7, not 2/5.

B. If there are 7 total players, and the ratio is 5 trumpets : 2 tubas, then trumpets are in fact 2.5 times the number of tuba players (2 tubas *2.5 = 5 trumpets).

C. The ratio is 5 trumpet players : 2 tuba players, not 2 trumpet players for every 5 tuba players.

D. The ratio of tubas to total number of tubas and trumpets is $\frac{2tuba}{7total}= \frac{t}{100total} \\ t=28.57 tubas$

5 0

4 years ago

What is the initial value of the function represented by this graph?

gladu [14]

The initial value of function is 2 or B.

5 0

3 years ago

Find the value of -8 + 9 · 2 ÷ -3. -2/3 -2 -11 -14

Viktor [21]

Answer:

the answer is D.14

Step-by-step explanation:

You do 9 ×2=18

18÷-3=-6

-8+-6=14

6 0

4 years ago

Assume that one day's labor in Argentina can produce either 20 units of cloth or 2 units of wine, while in Chile one day's labor

11111nata11111 [884]

Answer:

cloth production increase is 16 units

wine production increase is 8 units

Step-by-step explanation:

Given data

Argentina produce cloth = 20 units

Argentina produce wine = 2 units

chile produce cloth = 24 units

chile produce wine = 12 units

to find out

increase in combined output

solution

we know according to question Argentina transfers 2 units of labor from wine to cloth and Chile transfers 1 unit of labor from cloth to wine

therefore cloth production increase = Argentina produced total cloth - before transfer chile produce cloth ...........1

we can say that Argentina produced total cloth is 2 × 20 = 40 units

so from equation 1

cloth production increase = 40 - 24 = 16 units

cloth production increase is 16 units

and we now can say wine production increase = chile produce wine - before transfer Argentina produce wine .............2

so Chile produced total wine is 1 × 12 = 12 units

and Argentina produce wine with 2 units of labor (2 × 2) = 4

so from equation 2

wine production increase = 12 - 4 = 8 units

wine production increase is 8 units

8 0

4 years ago