Tabansi
2021-10-24
Answered

Construct a $3\times 3$ matrix A, with nonzero entries, and a vector b in $\mathbb{R}}^{3$ such that b is not in the set spanned by the columns of A.

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Sally Cresswell

Answered 2021-10-25
Author has **91** answers

For the matrix A in the result, any vector in the span of the column vectors is of the form on the left.

After multiply the scalars and adding the vectors, we get a vector of this form. Notice that all the entries vector are equal. Since the entries in vector b are not all same, 1,2,3,b cannot be in the span of the column vectors.

Result:

and

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Find a basis for the space of $2\times 2$ diagonal matrices.

$\text{Basis}=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

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Let B be a 4x4 matrix to which we apply the following operations:

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

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55 athletes are running race. A gold medal is to be given to the winer, a silver medal is to be given to the second-place finisher, and bronze medal is to be given to the third-place finisher. Asume that there are no ties. In how many possible ways can the 3 medals be distributed

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Find all z such that $|\mathrm{tan}z|=1$

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We want to find $O(x,y,z)$ by using two known points $P(2,3,5)$ and $Q(1,2,2)$ and angle of $POQ=60$ degrees with plane $E:1.15714286x+1.8547619y-z-2.86101191=0$ and length $OP=OQ$

Is there any way to find it?

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The reduced row echelon form of the matrix A is

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

Find three different such matrices A. Explain how you determined your matrices.

Find three different such matrices A. Explain how you determined your matrices.