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"As part of the 'Not Quite the Movies Challenge', here is an introduction to matrices."
15 Points Per Correct Answer - No time limit
A matrix is defined as a rectangular array of numbers or other elements. This means its shape (called its dimension) can be described by stating the number of rows and columns in which the elements are arranged. A matrix A is said to have dimension mxn. Which of the following statements about matrix A is true?
A has m rows and n columns
A has n rows and n columns
A has n rows and m columns
A has m rows and m columns
If a matrix A has dimension mxm, what kind of matrix is it?
A vector is a matrix for which there is only a single row or a single column. M is a 4x1 matrix, while N is a 1x4 matrix. Which of them could be described as a vector?
only M is a vector
both M and N are vectors
only N is a vector
neither N nor M is a vector
To add matrices, you simply add the corresponding elements. Which of the following is a pair of matrices that can be added?
A = ; B = 4 0
A = [1 2 3]; B = [4 -2]
A = [1 3]; B = [4 -2]
A = [1 3]; B = 4 -2 0]
How can you recognise an Additive Identity Matrix?
all elements are 1
all elements are 0
all elements add up to 0
all elements add up to 1
Multiplication involving matrices is a bit more complicated than it is with numbers. The cross product of two vectors, A x B, can only be calculated under what condition?
both matrices A and B have the same dimensions
the number of columns in A equals the number of rows in B
the number of rows in A equals the number of columns in B
both matrices A and B are vectors
Which familiar property of number calculations does NOT apply to matrix calculations, with a few exceptions? Assume that all operations indicated are in fact possible.
multiplicative commutavity, A x B = B x A
multiplicative associativity, A x (B x C) = (A x B) x C
additive commutativity, A + B = B + A
additive associativity, A + (B + C) = (A + B) + C
What is meant by the multiplicative inverse, A^-1, of a matrix A?
A + A^-1 gives a zero matrix
A x A^-1 gives a unit matrix
each element of A^-1 are equal to the corresponding element of A multiplied by -1
each elements of A^-1 is equal to the reciprocal of the corresponding element of A
Sometimes two vectors can be multiplied in such a way that the answer is a scalar (ordinary number), not a matrix. What is the name given to the result of this procedure?
How is the operation of matrix division (A divided by B) performed?
Divide each element of A by the corresponding element of B
It isn't defined as a matrix operation
Subtract each element of B from the corresponding element of A
Multiply each element of A by the reciprocal of the corresponding element of B
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Compiled Dec 04 13