Solution: We know that if two matrices are equal then the elements of each matrices are also equal. Given that two matrices are equal. Therefore by equating them we get, \[2a\text{ }+\text{ }b\text{...
Find x, y, a and b if
Solution: We know that if two matrices are equal then the elements of each matrices are also equal. Given that two matrices are equal. Therefore by equating them we get, \[2a\text{ }+\text{ }b\text{...
Find x, y, a and b if
Solution: 15. Given that two matrices are equal. We know that if two matrices are equal then the elements of each matrices are also equal. Therefore by equating them we get, \[3x\text{ }+\text{...
Construct a 4 × 3 matrix A = [ai j] whose elements ai j are given by: ai j = i
Given \[{{a}_{i\text{ }j}}~=\text{ }i\] Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{4\times 3}}\] So, the elements in a \[4\text{ }\times \text{ }3\] matrix are...
Construct a 4 × 3 matrix A = [ai j] whose elements ai j are given by: (i) ai j = 2i + i/j (ii) ai j = (i – j)/ (i + j)
(i) Given \[{{a}_{i\text{ }j}}~=\text{ }2i\text{ }+\text{ }i/j\] Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{4\times 3}}\] So, the elements in a \[4\text{ }\times \text{ }3\] matrix are...
Construct a 3×4 matrix A = [ai j] whose elements ai j are given by: ai j = ½ |-3i + j|
Given \[{{a}_{i\text{ }j}}~=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }\left| -3i\text{ }+\text{ }j \right|\] Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\times 3}}\] So, the elements in...
Construct a 3×4 matrix A = [ai j] whose elements ai j are given by: (i) ai j = 2i (ii) ai j = j
(i) Given \[{{a}_{i\text{ }j}}~=\text{ }2i\] Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\times 3}}\] So, the elements in a \[3\times 4\] matrix are \[{{a}_{11}},\text{ }{{a}_{12}},\text{...
Construct a 3×4 matrix A = [ai j] whose elements ai j are given by: (i) ai j = i + j (ii) ai j = i – j
(i) Given \[{{a}_{i\text{ }j}}~=\text{ }i\text{ }+\text{ }j\] Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\times 3}}\] So, the elements in a \[3\text{ }\times \text{ }4\]matrix are...
Construct a 2 × 2 matrix A = [ai j] whose elements ai j are given by: (i) ai j = (i – 2j)2 /2 (ii) ai j = (2i + j)2 /2
(i) Given \[{{a}_{i\text{ }j}}~=\text{ }{{\left( i\text{ }\text{ }2j \right)}^{2~}}/2\] Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\times 2}}\] So, the elements in a \[2\text{ }\times \text{...
Construct a 2 × 2 matrix A = [ai j] whose elements ai j are given by: (i) (i + j)2 /2 (ii) ai j = (i – j)2 /2
(i) Given \[{{\left( i\text{ }+\text{ }j \right)}^{2~}}/2\] Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\times 2}}\] So, the elements in a \[2\text{ }\times \text{ }2\] matrix are...
Construct a 2 ×3 matrix A = [aj j] whose elements aj j are given by: (i) ai j = i + j (ii) ai j = (i + j)2/2
(i) Given \[{{a}_{i\text{ }j~}}=\text{ }i\text{ }+\text{ }j\] Let \[A\text{ }=\text{ }[a{{~}_{i\text{ }j}}]{{~}_{2\times 3}}\] So, the elements in a \[2\text{ }\times \text{ }3\] matrix are...
Construct a 2 ×3 matrix A = [aj j] whose elements aj j are given by: (i) ai j = i × j (ii) ai j = 2i – j
(i) Given \[{{a}_{i\text{ }j}}~=\text{ }i\text{ }\times \text{ }j\] Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\text{ }\times \text{ }3}}\] So, the elements in a \[2\text{ }\times \text{...
Let A be a matrix of order 3 × 4. If R1 denotes the first row of A and C2 denotes its second column, then determine the orders of matrices R1 and C2.
Given A be a matrix of order \[3\text{ }\times \text{ }4\] So, \[A\text{ }=\text{ }[{{a}_{i\text{ }j}}]{{~}_{3\times 4}}\] \[{{R}_{1}}~=\text{ }first\text{ }row\text{ }of\text{ }A\text{ }=\text{...
Solve:
Solution: (i) Now, Comparing with equation (1) and (2) \[{{a}_{22}}~=\text{ }4\text{ }and\text{ }{{b}_{21}}~=\text{ }\text{ }3\] \[{{a}_{22}}~+\text{ }{{b}_{21}}~=\text{ }4\text{ }+\text{ }\left(...
If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?
If a matrix is of order \[m\text{ }\times \text{ }n\]elements, it has \[m\text{ }n\] elements. So, if the matrix has \[8\]elements, we will find the ordered pairs m and n. \[m\text{ }n\text{...