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What is a scalar matrix?

Back

A scalar matrix is a square matrix in which all the elements of the principal diagonal are equal and all other elements are zero.

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What is the result of adding two matrices?

Back

The result of adding two matrices is a new matrix where each element is the sum of the corresponding elements from the original matrices.

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How do you find the inverse of a matrix?

Back

To find the inverse of a matrix A, you can use the formula A^{-1} = rac{1}{det(A)} adj(A), where det(A) is the determinant of A and adj(A) is the adjugate of A.

Front

Back

The determinant of a 2x2 matrix A is calculated as det(A) = ad - bc.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.

Front

What is matrix subtraction?

Back

Matrix subtraction involves subtracting corresponding elements of two matrices of the same dimensions to produce a new matrix.

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

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How do you solve a system of linear equations using substitution?

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To solve a system using substitution, solve one equation for one variable and substitute that expression into the other equation(s).

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What is the result of multiplying a matrix by its inverse?

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The result of multiplying a matrix A by its inverse A^{-1} is the identity matrix: A A^{-1} = I.

Front

What is a scalar in the context of matrices?

Back

A scalar is a single number that can multiply a matrix, affecting all elements of the matrix equally.