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Question 1 of 5: Find the sum of A and B:
$$A=\left[ \begin{array}{cc}3 & -7\\ 5 & 2\end{array}\right]$$ $$B=\left[ \begin{array}{cc}-4 & 9\\ 2 & 1\end{array}\right]$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\left[ \begin{array}{cc}-1 & 2\\ 7 & 3\end{array}\right]$$
B
Does not exist
C
$$\left[ \begin{array}{cc}7 & -16\\ 3 & 1\end{array}\right]$$
D
$$\left[ \begin{array}{cc}-8 & 12\\ 11 & -5\end{array}\right]$$
E
$$\left[ \begin{array}{cc}5 & 6\\ -1 & 5\end{array}\right]$$
Question 2 of 5: Find the difference of A and B:
$$A=\left[ \begin{array}{ccc}2 & 9 & 1\\ 6 & -1 & 3\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}8 & -4 & 7\\ 12 & 3 & -2\end{array}\right]$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
Does not exist
B
$$\left[ \begin{array}{ccc}-6 & 13 & -6\\ 5 & -4 & -6\end{array}\right]$$
C
$$\left[ \begin{array}{ccc}-6 & 13 & -6\\ -6 & -4 & 5\end{array}\right]$$
D
$$\left[ \begin{array}{ccc}10 & 5 & 8\\ 18 & 2 & 1\end{array}\right]$$
E
$$\left[ \begin{array}{ccc}-2 & -9 & -1\\ -6 & 1 & -3\end{array}\right]$$
Question 3 of 5: Answer the given question:
Suppose we have two matrices: A and B. A is a 3 x 3 non-zero matrix (a matrix with at least one nonzero element). B is a 3 x 3 zero matrix (a matrix with all zeros as elements). Think about what happens if we add A and B together. What is the result of adding a non-zero matrix and a zero matrix of the same order together?
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
We get the zero matrix as our answer
B
We get the identity matrix as our answer
C
We get the inverse of the non-zero matrix
D
The non-zero matrix is unchanged
E
We get a singular matrix.
Question 4 of 5: Answer the given question:
$$A=\left[ \begin{array}{cc}9 & 2\\ -4 & 19 \\7 & -6\end{array}\right]$$ What is the result of A + (-A)?
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
The Identity Matrix
B
The Row-Column Jordan Matrix
C
The Zero Matrix
D
The Echelon Matrix
E
The Inverse Matrix
Question 5 of 5: Find X:
$$A=\left[ \begin{array}{ccc}20 & -15 & 7\\ 19 & 7 & -6\\18 & 8 & 2\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}11 & 17 & 1\\ 22 & 2 & -5\\35 & -6 & 3\end{array}\right]$$ A + X = B
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
No Solution
B
$$X=\left[ \begin{array}{ccc}-9 & 32 & -6\\ 3 & -5 & 1\\17 & -14 & 1\end{array}\right]$$
C
$$X=\left[ \begin{array}{ccc}9 & -32 & 6\\ -3 & 5 & -1\\-17 & 14 & -1\end{array}\right]$$
D
$$X=\left[ \begin{array}{ccc}1 & 0 & 0\\ 0 & 1 & 0\\0 & 0 & 1\end{array}\right]$$
E
$$X=\left[ \begin{array}{ccc}14 & -5 & 8\\ 23 & 5 & -1\\6 & -12 & 3\end{array}\right]$$

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