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3 years ago

Subtract the following polynomials. 3.1x + 2.8z 4.3x - 1.2z PLEASE HELP

Mathematics

1 answer:

Assoli18 [71]3 years ago

7 0

Answer:

3.1x+2.8z

3.1 over 10x +14 over 15 z

1 over 10 x (3.1x + 2.8z)

4.3x - 1.2z =

43 over 10x - 6 over 5z

1 over 10 x (43x-12z)

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For waht values of x do the vectors -1,0,-1), (2,1,2), (1,1, x) form a basis for R3?

DaniilM [7]

<h2>Answer:</h2>

The values of x for which the given vectors are basis for R³ is:

$x\neq 1$

<h2>Step-by-step explanation:</h2>

We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.

We are given three vectors as:

(-1,0,-1), (2,1,2), (1,1, x)

The matrix formed by these vectors is:

$\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right]$

Now, the determinant of this matrix is:

$\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-1(x-2)-2(1)+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+2-2+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+1$

Hence,

$-x+1\neq 0\\\\\\i.e.\\\\\\x\neq 1$

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Step-by-step explanation:

alice drew two triangles on the coordinate plane as shown. Which series of transformation proves the two triangles are congruent?

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