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The product of any matrix by the scalar ...

The product of any matrix by the scalar ......... Is the null matrix.

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To solve the question, we need to determine which scalar, when multiplied by any matrix, results in the null matrix (also known as the zero matrix). ### Step-by-Step Solution: 1. **Understanding the Null Matrix**: The null matrix, denoted as \( O \), is a matrix where all elements are zero. For example, a \( 2 \times 2 \) null matrix looks like this: \[ O = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} ...
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NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. Sum of two skew-symmetric matrices is always ......... Matrix.

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  2. The negative of a matrix is obtained b y multiplying it by ...........

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  3. The product of any matrix by the scalar ......... Is the null matrix.

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  4. A matrix which is not a square matrix is called a..........matrix.

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  5. Matrix multiplication is distributive over matrix addition

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  6. If A is a symmetric matrix , then A^(3) is a ........ Matrix.

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  7. If A is a skew-symmetric matrix, then A^(2) is a .................

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  8. If A and B are square matrices of the same order, then (i) (AB)=.......

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  9. If A is a skew-symmetric, then kA is a...........(where, k is any scal...

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  10. If A and B are symmetric matrices, then (i) AB-BA is a .......... ...

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  11. If A is symmetric matrix, then B'AB is............

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  12. If A and B are symmetric matrices of same order, then AB is symmetric ...

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  13. In applying one or more row operations while finding A^(-1) by elemen...

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  14. A matrix denotes a number

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  15. Matrices of any order can be added.

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  16. Two matrices are equal. If they have same number of rows and same numb...

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  17. Matrices of different order cannot be subtracted.

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  18. Matrix addition is associative as well as commutative.

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  19. Matrix m ultiplication is commutative.

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  20. A square m atrix where every element is unity is called an identity ma...

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