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CBSE Class 12 Math 2025 All Sets Solved Paper

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Question : 16 of 20
Marks: +1, -0
Let A=(1−2−104−1−321),B=(−2−5−7),C=[9,8,7],A = \begin{pmatrix} 1 & -2 & -1 \\ 0 & 4 & -1 \\ -3 & 2 & 1 \end{pmatrix}, B = \begin{pmatrix} -2 \\ -5 \\ -7 \end{pmatrix}, C=[9,8,7], which of the following is defined?
Solution:  
A=(1−2−104−1−321),B=(−2−5−7),C=[9,8,7]A = \begin{pmatrix} 1 & -2 & -1 \\ 0 & 4 & -1 \\ -3 & 2 & 1 \end{pmatrix}, B = \begin{pmatrix} -2 \\ -5 \\ -7 \end{pmatrix}, C=[9,8,7]
Order of A is 3×33 \times 3
Order of B is 3×13 \times 1
Order of C is 1×31 \times 3
Product of two matrices A and B is defined if the number of columns in matrix A is equal to number of rows in matrix B.
No. of column of matrix A = no. of rows of matrix B
∴ A B is defined
No. of column of matrix A = 3
∴ no. of row of matrix C = 1
∴ A C is not defined.
No. of column of matrix B is not equal to no. of rows matrix A.
So, BA is not defined.
No. of column of A is not equal to no. of row of C
∴ A C is not defined
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