Matrix L is a 3 ⨯ 5 matrix, matrix M is a 5 ⨯ 5 matrix, matrix N is a 3 ⨯ 3 matrix, and matrix P is a 5 ⨯ 3 matrix. Find the dimensions of the sums below, if they exist. (If an answer does not exist, enter DNE.) (a) L + M  _____ ⨯ _____ (b) L + PT  _____ ⨯ _____ (c) M + N  _____ ⨯ _____ (d) N + N  _____ ⨯ _____

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Matrix L is a 3 ⨯ 5 matrix, matrix M is a 5 ⨯ 5 matrix, matrix N is a 3 ⨯ 3 matrix, and matrix P is a 5 ⨯ 3 matrix. Find the dimensions of the sums below, if they exist. (If an answer does not exist, enter DNE.)

(a) L + M
 _____ ⨯ _____

(b) L + PT
 _____ ⨯ _____

(c) M + N
 _____ ⨯ _____

(d) N + N
 _____ ⨯ _____
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