Basic Operations - Matrices

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| By Merchyle
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1. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#183;«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mo»§nbsp;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mi»e«/mi»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»d«/mi»«/math»

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Basic Operations - Matrices - Quiz

This quiz will assess your understanding and skills in solving matrix problems.

2. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mn»2«/mn»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mn»9«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»9«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»11«/mn»«/mtd»«mtd»«mn»17«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

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3. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»6«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#183;«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»11«/mn»«/mtd»«mtd»«mn»13«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»27«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»29«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

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4. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mn»4«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#183;«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»48«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»24«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»24«/mn»«/mtd»«mtd»«mn»40«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

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5. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#183;«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»6«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»6«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#183;«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»68«/mn»«/mtd»«mtd»«mn»40«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»49«/mn»«/mtd»«mtd»«mn»26«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

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6. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»6«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»6«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»41«/mn»«/mtd»«mtd»«mn»53«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»23«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»27«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

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7. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»6«/mn»«mi»y«/mi»«/mtd»«mtd»«msup»«mi»y«/mi»«mn»2«/mn»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«mi»y«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«mi»y«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#183;«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mi»y«/mi»«/mtd»«mtd»«mi»x«/mi»«mi»y«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»6«/mn»«/mtd»«mtd»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»-«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»6«/mn»«mi»y«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»3«/mn»«mi»y«/mi»«/mtd»«mtd»«mi»y«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»12«/mn»«msup»«mi»y«/mi»«mi»y«/mi»«/msup»«mo»-«/mo»«mn»6«/mn»«mi»y«/mi»«/mtd»«mtd»«mn»6«/mn»«msup»«mi»y«/mi»«mn»2«/mn»«/msup»«mi»x«/mi»«mo»+«/mo»«msup»«mi»y«/mi»«mn»2«/mn»«/msup»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«msup»«mi»y«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»15«/mn»«mi»y«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«msup»«mi»y«/mi»«mn»2«/mn»«/msup»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«mi»y«/mi»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mi»y«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

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8. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»6«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#183;«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»6«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»17«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»37«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»16«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»9«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

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9. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»4«/mn»«mi»y«/mi»«/mtd»«mtd»«mn»2«/mn»«mi»y«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»2«/mn»«mi»y«/mi»«/mtd»«mtd»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»2«/mn»«mi»x«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mn»5«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mfenced close=¨]¨ open=¨[¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»20«/mn»«mi»y«/mi»«/mtd»«mtd»«mo»-«/mo»«mn»30«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»10«/mn»«mi»x«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

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10. A, B and C are matrices: A ( B + C ) = AB + CA

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The given equation states that the product of matrix A with the sum of matrices B and C is equal to the sum of the products of matrix A with B and matrix A with C. This equation is sometimes true because matrix multiplication is not commutative, meaning the order of multiplication matters. In some cases, the equation will hold true, but in others, it will not. Therefore, the statement "Sometimes true" is the correct answer.

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A, B and C are matrices: A ( B + C ) = AB + CA
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