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  • Choose the correct statement <img alt="\mathrm{A=\begin{bmatrix} x+2 &y^2+2 \\ -6& 0 \end{bmatrix},\;\;\;\;\;\;B=\begin{bmatrix} 2x+1 &3y \\ y^2-5y& 0 \end{bmatrix}}" src=

Choose the correct statement

\mathrm{A=\begin{bmatrix} x+2 &y^2+2 \\ -6& 0 \end{bmatrix},\;\;\;\;\;\;B=\begin{bmatrix} 2x+1 &3y \\ y^2-5y& 0 \end{bmatrix}}

Option: 1

If x=1, y=1 matrix A is equal to matrix B


Option: 2

If x=-\frac{1}{2} \;\;\text{and}\;\;y=0 matrix B is null matrix


Option: 3

Both are square matrix


Option: 4

All of the above


Answers (1)

best_answer

 

 

Types of Matrices - Part 1 -

Equal Matrices: Two matrices are said to be equal if they have the same order and each element of one matrix is equal to the corresponding elements of another matrix or we can say a_{ij}=b_{ij} where a is the element of one matrix and b is the element of another matrix.

 

-

 

 

option (a)

If matrix A is equal to matrix B then,

\\\mathrm{\begin{bmatrix} x+2 &y^2+2 \\ -6& 0 \end{bmatrix}=\begin{bmatrix} 2x+1 &3y \\ y^2-5y& 0 \end{bmatrix}}\\\\\mathrm{\Rightarrow x+2=2x+1\;\;\;\;\;\;\;\;\;\;\;\;\;\;....(i)}\\\mathrm{\:\;\;\;\; y^2+2=3y\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;....(ii)}\\\mathrm{\:\;\;\;-6=y^2-5y\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;....(iii)}\\\mathrm{\Rightarrow x=1\;\;\;\;[from\;\;eq(i)]}\\\mathrm{\;\;\;\;y=2\;\;or\;\;y=1\;\;\;\;[from\;eq(ii)]}\\\mathrm{\;\;\;\;y=2\;\;or\;\;y=3\;\;\;\;[from\;eq(iii)]}\\\mathrm{\Rightarrow x=1\;\;and\;\;y=2}

 

option (b)

put x=-\frac{1}{2} \;\;\text{and}\;\;y=0 in matrix B

\\B=\begin{bmatrix} 2x+1 &3y \\ y^2-5y& 0 \end{bmatrix}\\ \\\\B=\begin{bmatrix} 2(-\frac{1}{2})+1 &3(0) \\\\ (0)^2-5(0)& 0 \end{bmatrix}\\ \\\\B=\begin{bmatrix} 0 &0 \\ 0& 0 \end{bmatrix}

B is null matrix at x=-\frac{1}{2} \;\;\text{and}\;\;y=0

option (c)

Both matrices are of order 2x2

 

Hence all the statements are correct

correct option is (4)

Posted by

Rishi

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