floymdiT
2021-03-11
Answered

Use cramer's rule to determine the values of ${I}_{1},{I}_{2},{I}_{3}$ and ${I}_{4}$

$\left[\begin{array}{cccc}13.7& -4.7& -2.2& 0\\ -4.7& 15.4& 0& -8.2\\ -2.2& 0& 25.4& -22\\ 0& -8.2& -22& 31.3\end{array}\right]\left[\begin{array}{c}{I}_{1}\\ {I}_{2}\\ {I}_{3}\\ {I}_{4}\end{array}\right]=\left[\begin{array}{c}6\\ -6\\ 5\\ -9\end{array}\right]$

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asked 2021-02-08

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.

asked 2021-01-31

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

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

asked 2021-02-25

Find if possible the matrices:

a) AB b) BA.

$A=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right],B=\left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]$

a) AB b) BA.

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If the matrix X has a dimension of

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What are the trivial and non-trivial solution of homogeneous equations in the matrices?

asked 2022-02-13

Let $A=\left[\begin{array}{ccc}1& 0& -2\\ -2& 1& 6\\ 3& -2& -5\end{array}\right]$ and $b=\left[\begin{array}{c}-1\\ 7\\ -3\end{array}\right]$ . Define a linear transformation T by T(x)=AX. Determine a vector x whose image under T is b. Is the vector x that you found unique or not? Explain your answer.

asked 2020-12-25

For the given systems of linear equations, determine the values of ${b}_{1},{b}_{2},\text{and}{b}_{3}$ necessary for the system to be consistent. (Using matrices)

$x-y+3z={b}_{1}$

$3x-3y+9z={b}_{2}$

$-2x+2y-6z={b}_{3}$