Math Problem Statement
the matrix A is given as A = first collum is 1 0 3 second collum is 4 2-x -2 determine all values of x such that A^T equals first collum 10 -2 second collum -2 22
Solution
We are given the matrix as:
1 & 4 \\ 0 & 2 - x \\ 3 & -2 \end{pmatrix}$$ And we're asked to determine the values of $$x$$ such that the transpose of $$A$$ equals: $$A^T = \begin{pmatrix} 10 & -2 \\ -2 & 22 \end{pmatrix}$$ ### Step 1: Recall the definition of a matrix transpose. The transpose of a matrix $$A$$, denoted $$A^T$$, is formed by flipping the matrix over its diagonal. This means that the rows of $$A$$ become the columns of $$A^T$$. Thus, the transpose of $$A$$ is: $$A^T = \begin{pmatrix} 1 & 0 & 3 \\ 4 & 2 - x & -2 \end{pmatrix}$$ ### Step 2: Compare $$A^T$$ with the given matrix. We are given: $$A^T = \begin{pmatrix} 10 & -2 \\ -2 & 22 \end{pmatrix}$$ Now, let's compare each entry: - From the first column: - $$1 = 10$$ (which is inconsistent) - $$0 = -2$$ (which is inconsistent) - $$3 = 22$$ (which is inconsistent) We realize there is some inconsistency here. Could you clarify if you meant to state the original matrix differently? I feel there might have been a misunderstanding. Please let me know if any details need adjusting.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Transpose
Linear Algebra
Formulas
Transpose of a matrix: A^T[i][j] = A[j][i]
Theorems
Definition of Matrix Transpose
Suitable Grade Level
Grades 9-11
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