# ▸ Linear Algebra :

1. Let two matrices be
,
What is A - B ?

1. Let two matrices be
,
What is A + B ?

1. Let

What is 2∗x ?

• Correct
To multiply the vector x by 2, take each element of x and multiply that element by 2.

1. Let

What is 2∗x ?

• Correct
To multiply the vector x by 2, take each element of x and multiply that element by 2.

1. Let u be a 3-dimensional vector, where specifically

What is ?

1. Let u and v be 3-dimensional vectors, where specifically

and

what is ?
(Hint: is a 1x3 dimensional matrix, and v can also be seen as a 3x1 matrix. The answer you want can be obtained by taking the matrix product of and .) Do not add brackets to your answer.
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1. Let A and B be 3x3 (square) matrices. Which of the following must necessarily hold true? Check all that apply.

• If A is the 3x3 identity matrix, then
Correct
Even though matrix multiplication is not commutative in general ( for general matrices A,B), for the special case where , we have , and also . So, .

• Correct
We add matrices element-wise. So, this must be true.

1. Let A and B be 3x3 (square) matrices. Which of the following must necessarily hold true? Check all that apply.
• If , then C is a 3x3 matrix.
Correct
• If A is the 3x3 identity matrix, then
Correct
Even though matrix multiplication is not commutative in general ( for general matrices A,B), for the special case where , we have , and also . So, .

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