If two matrices, A and B, are equal, which of the
following statements are true?
O Matrix Almust be a diagonal matrix.
O Both matrices must be square.
Both matrices must be the same size.
For any value of i, j; aj = bij.

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Аноним Аноним · Answer 1 · 2019-10-03T09:28:06+02:00

If A and B are equal:

Matrix A must be a diagonal matrix: FALSE.

We only know that A and B are equal, so they can both be non-diagonal matrices. Here's a counterexample:

[tex]A=B=\left[\begin{array}{cc}1&2\\4&5\\7&8\end{array}\right][/tex]

Both matrices must be square: FALSE.

We only know that A and B are equal, so they can both be non-square matrices. The previous counterexample still works

Both matrices must be the same size: TRUE

If A and B are equal, they are literally the same matrix. So, in particular, they also share the size.

For any value of i, j; aij = bij: TRUE

Assuming that there was a small typo in the question, this is also true: two matrices are equal if the correspondent entries are the same.

MrRoyal MrRoyal · Answer 2 · 2022-01-07T15:41:03+01:00

Matrices represent their data in rows and columns.

The true options are:

The names of the matrices are given as:

A and B

For any two matrices to be equal, then the following must be true:

The above highlights mean that:

If matrix A is 2 by 3, then matrix B must also be 2 by 3
If the element at A[i][j] is 5, then the element at B[i][j] must also be 5

Hence, the true options are (c) and (d)