Q: How do you verify solution of matrices in 3x3 matrix?

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If you mean what does something like SL(3, R) mean, it is the group of all 3X3 matrices with determinant 1, with real entries, under matrix multiplication.

Yes, the result is a 3x3 matrix

It is the product of the three diagonal elements.

You can only add a 3x3 matrix to another matrix of the same size. The reuslt is a 3x3 matrix where each element is the sum of the elements in the corresponding positions in the two summand matrices.Symbolically,if A = {aij} and B = {bij} then A + B = {aij + bij}where i=1,2,3 and j = 1,2,3

3-x,-1,1, -1,5-x,-1 1,-1,3-x

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A 3x3 matrix has 9 elements. If each element can be either 0 or 1 only (two options) then there are 2^9 = 512 possibilities.

If you mean what does something like SL(3, R) mean, it is the group of all 3X3 matrices with determinant 1, with real entries, under matrix multiplication.

Yes, the result is a 3x3 matrix

A minor is a determinant and a determinant is a value associated with a square matrix.The matrix from which a minor is calculated is formed from a matrix by removing at least one of its rows or columns.We are discussing matrices of 3 rows and 4 columns. The minimum change one can make is to remove a single column. This can be done in four ways, yielding four minors. Each of these four ways yields a 3x3 matrix. There are nine minors in a 3x3 matrix.Hence, the total number of minors is 4 + 4(9)=40.

It is the product of the three diagonal elements.

for a 3x3 matrix, it can be interpreted as the volume of the hexahedron formed by three vectors (each row of the matrix as one vector).

It is the product of the three diagonal elements.

Assuming the matrix is a 3x3 matrix of 1-digit number, it is 23. Otherwise it depends on how the 9 digits split up.

for a 3x3 matrix, it can be interpreted as the volume of the hexahedron formed by three vectors (each row of the matrix as one vector).

You can only add a 3x3 matrix to another matrix of the same size. The reuslt is a 3x3 matrix where each element is the sum of the elements in the corresponding positions in the two summand matrices.Symbolically,if A = {aij} and B = {bij} then A + B = {aij + bij}where i=1,2,3 and j = 1,2,3

First of all, if we have any two matrices of sizes mxn and pxq where m, n, p and q are natural numbers, then we must have n=p to be able to multiply the matrices. The result is an mxq matrix. For example, a 3x1 matrix has m=3 and n=1. We can multiply it with any matrix of size 1xq. For example a 2x3 matrix can be multiplied with a 3x1 matrix which has 3 rows and 1 column and the result is a 2x1 matrix. (2x3) multiplies by (3x1) gives a (2x1) matrix. The easy way to remember this is write the dimension of Matrix A and then Matrix B. The two inner numbers must be the same and the two outer numbers are the dimensions of the matrix you have after multiplication. For example Let Matrix A have dimensions (axb) multiply it by matrix B which has dimensions (bxc) = the result is matrix of dimensions ac. Using the trick we would remind ourselves by writing (a,b)x(b,c)=(a,c). This is technically wrong because the numbers are dimensions, but it is just a method to help students remember how to do it. So, a 3x3 matrix can be multiplied by a 3x 1 but not by a 1,3 matrix. How do you do it? Just multiply each entry in the first row of A by each entry in the first column of B and add the products. Do the same for the next row etc. Many (or should I honestly say MOST) people use their fingers and go along row one and then down column one. The add the products of the entries as they do that. Then they do the same for row two and column two etc. It really does help!

3-x,-1,1, -1,5-x,-1 1,-1,3-x