How would you solve the following Matrices question?

johnthoma_s

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Question 3

(a) Given the matrix A = [3 2 4], determine B = ATA and C = AAT. Find the determinants and inverses of B and C.

(b) If D = EF, find d45 (i.e., the element in the fourth row and the fifth column of the matrix), given:


. . . . .\(\displaystyle E\, =\, \left[\begin{array}{ccc}3&6&8\\1&2&4\\5&6&5\\3&6&8\\1&2&4\\5&6&5 \end{array}\right]\, \mbox{ and }\, F\, =\, \left[\begin{array}{cccccc}3&5&8&3&6&8\\9&2&4&7&2&4\\5&6&5&5&6&5 \end{array}\right]\)

(c) Given the vector a = i + 2j - 2k, find the possible set of values for y and z such that b = yj + zk is a unit vector perpendicular to a.



thanks all, really need the help! i did it on my own but the answer doesn't exactly seem to make sense to me. So would like a different point of view. Appreciate the help :)
 

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Question 3

(a) Given the matrix A = [3 2 4], determine B = ATA and C = AAT. Find the determinants and inverses of B and C.

(b) If D = EF, find d45 (i.e., the element in the fourth row and the fifth column of the matrix), given:


. . . . .\(\displaystyle E\, =\, \left[\begin{array}{ccc}3&6&8\\1&2&4\\5&6&5\\3&6&8\\1&2&4\\5&6&5 \end{array}\right]\, \mbox{ and }\, F\, =\, \left[\begin{array}{cccccc}3&5&8&3&6&8\\9&2&4&7&2&4\\5&6&5&5&6&5 \end{array}\right]\)

(c) Given the vector a = i + 2j - 2k, find the possible set of values for y and z such that b = yj + zk is a unit vector perpendicular to a.



thanks all, really need the help! i did it on my own but the answer doesn't exactly seem to make sense to me. So would like a different point of view. Appreciate the help :smile:

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