Let A be a 3x2 matrix B be a 2x3 matrix C be a 2x2 identity matrix D be a 2x2 no

Question

Let A be a 3x2 matrix B be a 2x3 matrix C be a 2x2 identity matrix D be a 2x2 nonsingular matrix I be the 2x2 singular matrix.
Clearly Circle either True or False for each of the statmentsbelow? and explain why?

(a) T or F It is possible to compute: CB+AT
(b) T or F It is possible to compute: CBA=BA
(c) T or F It is possible to compute:DD-1=C
(d) T or F It is possible to compute: AE-1 +A
(e) T or F it is possible to compute: EDCBA
B be a 2x3 matrix C be a 2x2 identity matrix D be a 2x2 nonsingular matrix I be the 2x2 singular matrix.
Clearly Circle either True or False for each of the statmentsbelow? and explain why?

(a) T or F It is possible to compute: CB+AT
(b) T or F It is possible to compute: CBA=BA
(c) T or F It is possible to compute:DD-1=C
(d) T or F It is possible to compute: AE-1 +A
(e) T or F it is possible to compute: EDCBA


(a) T or F It is possible to compute: CB+AT
(b) T or F It is possible to compute: CBA=BA
(c) T or F It is possible to compute:DD-1=C
(d) T or F It is possible to compute: AE-1 +A
(e) T or F it is possible to compute: EDCBA

(a) T or F It is possible to compute: CB+AT (b) T or F It is possible to compute: CBA=BA (c) T or F It is possible to compute:DD-1=C (d) T or F It is possible to compute: AE-1 +A
(e) T or F it is possible to compute: EDCBA

Explanation / Answer

(a) True       Since C is a 2*2 matrixand B is a 2*3 matrix, CB is a 2*3 matrix       A is 3*2 matrix, itstranspose is a 2*3 matirx. Since CB and A have the same number ofrows and columns it is possible to calculateCB+AT (b) True    As already discussed it is possible tocalculate CB. Also since C is an identity matrix, CB = C    Hence, CBA = BA. It is possible to multiplyB and a since the number of columns in B is the same as the numberof rows in A. (c) True    By definition, an inverse matrix is thatwhich on multiplication with the original matrix gives an identitymatrix (d) False    Since E is a singular matrix, E-1 cannot becalculated (e) True        (b) True    As already discussed it is possible tocalculate CB. Also since C is an identity matrix, CB = C    Hence, CBA = BA. It is possible to multiplyB and a since the number of columns in B is the same as the numberof rows in A. (c) True    By definition, an inverse matrix is thatwhich on multiplication with the original matrix gives an identitymatrix (d) False    Since E is a singular matrix, E-1 cannot becalculated (e) True       

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